A057145 - OEIS

This site is supported by donations to The OEIS Foundation.

A057145

Square array T(n,k) of polygonal numbers T(n,k) = ((n-2)*k^2-(n-4)*k)/2, n >= 2, k >= 1, read by antidiagonals.

1, 1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 9, 10, 5, 1, 6, 12, 16, 15, 6, 1, 7, 15, 22, 25, 21, 7, 1, 8, 18, 28, 35, 36, 28, 8, 1, 9, 21, 34, 45, 51, 49, 36, 9, 1, 10, 24, 40, 55, 66, 70, 64, 45, 10, 1, 11, 27, 46, 65, 81, 91, 92, 81, 55, 11 (list; table; graph; refs; listen; history; internal format)

	OFFSET	`2,3`
	COMMENTS	`T(2n+4,n) = n^3 [Stuart M. Ellerstein (ELLERSTEIN(AT)aol.com), Aug 28, 2000]`
	REFERENCES	`A. H. Beiler, Recreations in the Theory of Numbers. New York: Dover, p. 189, 1966.`
	FORMULA	`T(n, k) = T(n-1, k)+k(k-1)/2 [with T(2, k)=k] =T(n, k-1)+1+(n-2)(k-1) [with T(n, 0)=0] = k+(n-2)k(k-1)/2 =k+A063212(n-2, k-1) - Henry Bottomley, Jul 11 2001` `G.f. for row n: (1+(n-3)*x)/(1-x)^3, n>=2. - Paul Barry, Feb 21 2003`
	EXAMPLE	`Array (n >= 2, k >= 1) begins:` `1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...` `1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, ...` `1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, ...` `1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, ...` `1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, ...` `1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, ...` `1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, ...` `1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 396, ...` `1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451, ...` `1, 11, 30, 58, 95, 141, 196, 260, 333, 415, 506, ...` `1, 12, 33, 64, 105, 156, 217, 288, 369, 460, 561, ...` `1, 13, 36, 70, 115, 171, 238, 316, 405, 505, 616, ...` `1, 14, 39, 76, 125, 186, 259, 344, 441, 550, 671, ...`
	MATHEMATICA	`t[n_, k_] := ((n-2)k^2 - (n-4)k)/2; max = 12; m = Table[t[n, k], {n, 2, max}, {k, 1, max-1}]; Flatten[ Table[ Reverse @ Diagonal[ Reverse /@ m, k], {k, max-2, -max+2, -1}]] (* From Jean-François Alcover, Jul 21 2011 *)`
	CROSSREFS	`Many rows and columns of this array are in the database.` `Antidiagonal sums form A055795.` `Sequence in context: A093430 A074659 A131251 * A134394 A074909 A135278` `Adjacent sequences: A057142 A057143 A057144 * A057146 A057147 A057148`
	KEYWORD	`nonn,nice,tabl,easy`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), Sep 12 2000`
	EXTENSIONS	`Jul 22 2011 : a(50)=49 corrected to a(50)=40 by Jean-François Alcover`

Content is available under The OEIS End-User License Agreement .

Last modified February 15 08:20 EST 2012. Contains 205729 sequences.