A centered square number is a centered figurate number that represents a square with a dot in the center and all other dots surrounding the center up to a certain city block distance, i.e. a diagonal square region of a square lattice, or an upright square region of a "centered square lattice". Like this: Centred numbers are class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides. ... A figurate number is a number that can be represented as a regular and discrete geometric pattern (e. ... A square as a geometric shape is described and illustrated at square (geometry). ... Manhattan distance sample: the three routes (red, blue, yellow) between the two points have the same length Taxicab geometry, considered by Hermann Minkowski in the 19th century, is a form of geometry in which the usual metric of Euclidean geometry is replaced by a new metric in which the distance... Upright square tiling. ...

 * * * * *** *** *** * ***** ***** *** ******* * ***** *** * 

The centered square number for n is given by the formula

n² + (n − 1)².

In other words, a centered square number is the sum of two consecutive square numbers. The following pattern demonstrates this formula: In mathematics, a square number, sometimes also called a perfect square, is an integer that can be written as the square of some other integer. ...

 X X X X X0X X0X X0X X X0X0X X0X0X X0X X0X0X0X X X0X0X X0X X 

The formula can also be expressed as

but n has to be odd in this case.

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The first few centered square numbers are

1, 5, 13, 25, 41, 61, 85, 113, 145, 181, 221, 265, 313, 365, 421, 481, 545, 613, 685, 761, 841, 925, 1013, 1105, 1201, 1301, 1405, 1513, 1625, 1741, 1861, 1985, 2113, 2245, 2381, 2521, 2665, 2813, 2965, 3121, 3281, 3445, 3613, 3785, 3961, 4141, 4325 Look up one on Wiktionary, the free dictionary. ... 5 (five) is a number, numeral, and glyph. ... Thirteen redirects here. ... 25 (twenty-five) is the natural number following 24 and preceding 26. ... 41 is the natural number following 40 and preceding 42. ... 61 (sixty-one) is the natural number following 60 and preceding 62. ... 85 is the natural number following 84 and preceding 86. ... 113 is the natural number following 112 and preceding 114. ... 145 is the natural number following 144 and preceding 146. ... 365 is a semiprime centered square number. ...

All centered square numbers are odd, and in base 10 one can notice the one's digits follows the pattern 1-5-3-5-1.

All centered square numbers and their divisors have a remainder of one when divided by four. Hence all centered square numbers and their divisors end with digits 1 or 5 in base 6, 8 or 12. A senary numeral system is a base-six numeral system. ... The octal numeral system is the base-8 number system, and uses the digits 0 to 7. ... A duodecimal multiplication table The duodecimal (also known as base-twelve or dozenal) system is a numeral system using twelve as its base. ...

Centered square prime

A centered square prime is a centered square number that is prime. The first few centered square primes are In mathematics, a prime number (or prime) is a natural number greater than one whose only positive divisors are one and itself. ...

5, 13, 41, 61, 113, 181, 313, 421, ....

See also: regularajjajahahah

• (n^2 + 1) / 2 as a special case of M(i,j) = (i^2 + j) / 2