Term

Centered Square

Centered figurate numbers — a dot ringed by squares: k² + (k−1)² → 1, 5, 13, 25, 41, 61, 85, ….

84 numbers tagged.

A centered square number counts dots in a square with a dot at the centre and successive square rings around it: 1, 5, 13, 25, 41, 61, 85, 113. Each equals the sum of two consecutive squares, \(k^2 + (k-1)^2\), and also equals \(4 \times\) a [[triangular]] number plus 1.

They are the centered cousins of the ordinary [[square]] numbers, and they appear in the cross-section of a square-packed pyramid. The differences between consecutive centered square numbers are the multiples of four.

5 13 25 41 61 85 113 145 181 221 265 313 365 421 481 545 613 685 761 841 925 1,013 1,105 1,201 1,301 1,405 1,513 1,625 1,741 1,861 1,985 2,113 2,381 2,521 3,121 3,613 4,513 5,101 7,321 8,581 9,661 9,941 10,513 12,641 13,613 14,281 14,621 15,313 16,381 19,013 19,801 20,201 21,013 21,841 23,981 24,421 26,681 30,013 34,061 36,721 37,813 38,921 41,761 44,701 47,741 49,613 51,521 52,813 54,121 56,113 59,513 60,901 68,821 70,313 71,821 76,441 79,601 82,013 83,641 86,113 90,313 94,613 97,241 99,013

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