A317302 - OEIS

A317302

Square array T(n,k) = (n - 2)*(k - 1)*k/2 + k, with n >= 0, k >= 0, read by antidiagonals upwards.

0, 0, 1, 0, 1, 0, 0, 1, 1, -3, 0, 1, 2, 0, -8, 0, 1, 3, 3, -2, -15, 0, 1, 4, 6, 4, -5, -24, 0, 1, 5, 9, 10, 5, -9, -35, 0, 1, 6, 12, 16, 15, 6, -14, -48, 0, 1, 7, 15, 22, 25, 21, 7, -20, -63, 0, 1, 8, 18, 28, 35, 36, 28, 8, -27, -80, 0, 1, 9, 21, 34, 45, 51, 49, 36, 9, -35, -99, 0, 1, 10, 24, 40, 55, 66 (list; table; graph; refs; listen; history; text; internal format)

	OFFSET	`0,10`
	COMMENTS	`Note that the formula gives several kinds of numbers, for example:` `Row 0 gives 0 together with A258837.` `Row 1 gives 0 together with A080956.` `Row 2 gives A001477, the nonnegative numbers.` `For n >= 3, row n gives the n-gonal numbers (see Crossrefs section).`
	LINKS	`Table of n, a(n) for n=0..84.` `Omar E. Pol, Polygonal numbers.` `The OEIS, Polygonal numbers.` `University of Surrey, Dept. of Mathematics, Polygonal Numbers - or Numbers as Shapes.` `Eric Weisstein's World of Mathematics, Figurate Number.` `Eric Weisstein's World of Mathematics, Polygonal Number.` `Wikipedia, Polygonal number.` `Index to sequences related to polygonal numbers`
	FORMULA	`T(n,k) = A139600(n-2,k) if n >= 2.` `T(n,k) = A139601(n-3,k) if n >= 3.`
	EXAMPLE	`Array begins:` `------------------------------------------------------------------------` `n\k Numbers Seq. No. 0 1 2 3 4 5 6 7 8` `------------------------------------------------------------------------` `0 ............ (A258837): 0, 1, 0, -3, -8, -15, -24, -35, -48, ...` `1 ............ (A080956): 0, 1, 1, 0, -2, -5, -9, -14, -20, ...` `2 Nonnegatives A001477: 0, 1, 2, 3, 4, 5, 6, 7, 8, ...` `3 Triangulars A000217: 0, 1, 3, 6, 10, 15, 21, 28, 36, ...` `4 Squares A000290: 0, 1, 4, 9, 16, 25, 36, 49, 64, ...` `5 Pentagonals A000326: 0, 1, 5, 12, 22, 35, 51, 70, 92, ...` `6 Hexagonals A000384: 0, 1, 6, 15, 28, 45, 66, 91, 120, ...` `7 Heptagonals A000566: 0, 1, 7, 18, 34, 55, 81, 112, 148, ...` `8 Octagonals A000567: 0, 1, 8, 21, 40, 65, 96, 133, 176, ...` `9 9-gonals A001106: 0, 1, 9, 24, 46, 75, 111, 154, 204, ...` `10 10-gonals A001107: 0, 1, 10, 27, 52, 85, 126, 175, 232, ...` `11 11-gonals A051682: 0, 1, 11, 30, 58, 95, 141, 196, 260, ...` `12 12-gonals A051624: 0, 1, 12, 33, 64, 105, 156, 217, 288, ...` `13 13-gonals A051865: 0, 1, 13, 36, 70, 115, 171, 238, 316, ...` `14 14-gonals A051866: 0, 1, 14, 39, 76, 125, 186, 259, 344, ...` `15 15-gonals A051867: 0, 1, 15, 42, 82, 135, 201, 280, 372, ...` `...`
	CROSSREFS	`Column 0 gives A000004.` `Column 1 gives A000012.` `Column 2 gives A001477, which coincides with the row numbers.` `Main diagonal gives A060354.` `Row 0 gives 0 together with A258837.` `Row 1 gives 0 together with A080956.` `Row 2 gives A001477, the same as column 2.` `For n >= 3, row n gives the n-gonal numbers: A000217 (n=3), A000290 (n=4), A000326 (n=5), A000384 (n=6), A000566 (n=7), A000567 (n=8), A001106 (n=9), A001107 (n=10), A051682 (n=11), A051624 (n=12), A051865 (n=13), A051866 (n=14), A051867 (n=15), A051868 (n=16), A051869 (n=17), A051870 (n=18), A051871 (n=19), A051872 (n=20), A051873 (n=21), A051874 (n=22), A051875 (n=23), A051876 (n=24), A255184 (n=25), A255185 (n=26), A255186 (n=27), A161935 (n=28), A255187 (n=29), A254474 (n=30).` `Cf. A139600, A139601.` `Cf. A303301 (similar table but with generalized polygonal numbers).` `Sequence in context: A124027 A097610 A161556 * A242869 A224878 A129555` `Adjacent sequences: A317299 A317300 A317301 * A317303 A317304 A317305`
	KEYWORD	`sign,tabl,easy`
	AUTHOR	`Omar E. Pol, Aug 09 2018`
	STATUS	`approved`