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 A177993 Triangle read by rows, A177990 * A007318. 4
 1, 1, 1, 2, 3, 1, 2, 4, 3, 1, 3, 8, 9, 5, 1, 3, 9, 13, 11, 5, 1, 4, 15, 28, 31, 20, 7, 1, 4, 16, 34, 46, 40, 22, 7, 1, 5, 24, 62, 102, 110, 78, 35, 9, 1, 5, 25, 70, 130, 166, 148, 91, 37, 9, 1, 6, 35, 115, 250, 376, 400, 301, 157, 54, 11, 1, 6, 36, 125, 295, 496, 610, 553, 367, 174, 56, 11, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50) FORMULA As infinite lower triangular matrices, A177990 * Pascal's triangle, (A007318). T(n,k) = binomial(n,k) + Sum_{j=0..floor(n/2)-1} binomial(2*j+1,k). - Andrew Howroyd, Apr 13 2021 EXAMPLE First few rows of the triangle = 1; 1, 1; 2, 3, 1; 2, 4, 3, 1; 3, 8, 9, 5, 1; 3, 9, 13, 11, 5, 1; 4, 15, 28, 31, 20, 7, 1; 4, 16, 34, 46, 40, 22, 7, 1; 5, 24, 62, 102, 110, 78, 35, 9, 1; 5, 25, 70, 130, 166, 148, 91, 37, 9, 1; 6, 35, 115, 250, 376, 400, 301, 157, 54, 11, 1; 6, 36, 125, 295, 496, 610, 553, 367, 174, 56, 11, 1; 7, 48, 191, 515, 991, 1402, 1477, 1159, 669, 276, 77, 13, 1; 7, 49, 203, 581, 1211, 1897, 2269, 2083, 1461, 771, 297, 709, 13, 1; ... PROG (PARI) T(n, k) = {binomial(n, k) + sum(j=0, n\2-1, binomial(2*j+1, k))} \\ Andrew Howroyd, Apr 13 2021 CROSSREFS Row sums are A061547(n+1). Cf. A177992 = A007318 * A177990. Cf. A061547. Sequence in context: A233359 A279345 A097966 * A256990 A071503 A029271 Adjacent sequences: A177990 A177991 A177992 * A177994 A177995 A177996 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, May 16 2010 EXTENSIONS Terms a(55) and beyond from Andrew Howroyd, Apr 13 2021 STATUS approved

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Last modified November 28 07:39 EST 2023. Contains 367394 sequences. (Running on oeis4.)