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 A081422 Triangle read by rows in which row n consists of the first n+1 n-gonal numbers. 9
 1, 1, 1, 1, 2, 3, 1, 3, 6, 10, 1, 4, 9, 16, 25, 1, 5, 12, 22, 35, 51, 1, 6, 15, 28, 45, 66, 91, 1, 7, 18, 34, 55, 81, 112, 148, 1, 8, 21, 40, 65, 96, 133, 176, 225, 1, 9, 24, 46, 75, 111, 154, 204, 261, 325, 1, 10, 27, 52, 85, 126, 175, 232, 297, 370, 451 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS T. D. Noe, Rows n = 0..100 of triangle, flattened Eric Weisstein's World of Mathematics, Polygonal Number FORMULA Array of coefficients of x in the expansions of T(k, x) = (1 + k*x -(k-2)*x^2)/(1-x)^4, k > -4. T(n, k) = k*((n-2)*k -(n-4))/2 (see MathWorld link). - Michel Marcus, Jun 22 2015 EXAMPLE The array starts   1  1  3 10 ...   1  2  6 16 ...   1  3  9 22 ...   1  4 12 28 ... The triangle starts   1;   1,  1;   1,  2,  3;   1,  3,  6, 10;   1,  4,  9, 16, 25;   ... MATHEMATICA Table[PolygonalNumber[n, i], {n, 0, 10}, {i, n+1}]//Flatten (* Requires Mathematica version 10.4 or later *) (* Harvey P. Dale, Aug 27 2016 *) PROG (PARI) tabl(nn) = {for (n=0, nn, for (k=1, n+1, print1(k*((n-2)*k-(n-4))/2, ", "); ); print(); ); } \\ Michel Marcus, Jun 22 2015 (MAGMA) [[k*((n-2)*k-(n-4))/2: k in [1..n+1]]: n in [0..10]]; // G. C. Greubel, Oct 13 2018 (Sage) [[k*((n-2)*k -(n-4))/2 for k in (1..n+1)] for n in (0..10)] # G. C. Greubel, Aug 14 2019 (GAP) Flat(List([0..10], n-> List([1..n+1], k-> k*((n-2)*k-(n-4))/2 ))); # G. C. Greubel, Aug 14 2019 CROSSREFS Rows include A060354, A064808, A000600, A000603, A002411. Diagonals include A001093, A053698, A069778, A000578, A002414, A081423, A081435, A081436, A081437, A081438, A081441. Antidiagonals are composed of n-gonal numbers. Sequence in context: A208516 A111808 A247046 * A213742 A213743 A213744 Adjacent sequences:  A081419 A081420 A081421 * A081423 A081424 A081425 KEYWORD easy,nonn,tabl,look AUTHOR Paul Barry, Mar 21 2003 STATUS approved

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)