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 A029656 Numbers in the (2,1)-Pascal triangle A029653 that are different from 1. 2
 2, 2, 3, 2, 5, 4, 2, 7, 9, 5, 2, 9, 16, 14, 6, 2, 11, 25, 30, 20, 7, 2, 13, 36, 55, 50, 27, 8, 2, 15, 49, 91, 105, 77, 35, 9, 2, 17, 64, 140, 196, 182, 112, 44, 10, 2, 19, 81, 204, 336, 378, 294, 156, 54, 11, 2, 21, 100, 285, 540, 714, 672, 450, 210, 65, 12, 2, 23, 121, 385 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 REFERENCES D. M. Bressoud, Proofs and Confirmations, Camb. Univ. Press, 1999; triangle on page 6, numerators. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150) Eric Weisstein's World of Mathematics, Alternating Sign Matrix. D. Zeilberger, Dave Robbins's Art of Guessing, Adv. in Appl. Math. 34 (2005), 939-954. FORMULA From Thomas Baruchel, Jun 26 2018: (Start) a(n,k) = (binomial(n+2,k+1) + binomial(n+1,k) + binomial(n,k) - binomial(n,k+1))/2. a(n,k) = binomial(n-1,k-1) + binomial(n-1,k) + binomial(n,k-1) + binomial(n,k). (End) EXAMPLE Triangle begins: 2; 2, 3; 2, 5, 4; 2, 7, 9, 5; 2, 9, 16, 14, 6; 2, 11, 25, 30, 20, 7; ... MATHEMATICA Table[(Binomial[n + 2, k + 1] + Binomial[n + 1, k] + Binomial[n, k] - Binomial[n, k + 1])/2, {n, 0, 11}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jun 29 2018 *) CROSSREFS Cf. A048601, A029638. Sequence in context: A307687 A281121 A220949 * A121306 A073311 A347560 Adjacent sequences: A029653 A029654 A029655 * A029657 A029658 A029659 KEYWORD nonn,tabl AUTHOR Mohammad K. Azarian EXTENSIONS More terms from James A. Sellers STATUS approved

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Last modified June 25 10:28 EDT 2024. Contains 373701 sequences. (Running on oeis4.)