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 A172185 (9,11) Pascal triangle. 2
 1, 9, 11, 9, 20, 11, 9, 29, 31, 11, 9, 38, 60, 42, 11, 9, 47, 98, 102, 53, 11, 9, 56, 145, 200, 155, 64, 11, 9, 65, 201, 345, 355, 219, 75, 11, 9, 74, 266, 546, 700, 574, 294, 86, 11, 9, 83, 340, 812, 1246, 1274, 868, 380, 97, 11, 9, 92, 423, 1152, 2058, 2520, 2142, 1248, 477, 108, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sums of NW-SE diagonals give A022114 (apart from first two terms). Triangle T(n,k), read by rows, given by (9,-8,0,0,0,0,0,0,0,...) DELTA (11,-10,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 09 2011 Row n: Expansion of (9+11x)*(1+x)^(n-1), n > 0. - Philippe Deléham, Oct 09 2011 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n,k) = T(n-1,k-1) + T(n-1,k) with T(0,0)=1, T(1,0)=9, T(1,1)=11. - Philippe Deléham, Oct 09 2011 G.f.: (1+8*x+10*y*x)/(1-x-y*x). - Philippe Deléham, Apr 13 2012 From G. C. Greubel, Apr 28 2022: (Start) T(n, k) = 9*binomial(n, k) + 2*binomial(n-1, k-1) with T(0, 0) = 1. Sum_{k=0..n} T(n, k) = 10*2^n - 9*[n=0]. (End) EXAMPLE Triangle begins: 1; 9, 11; 9, 20, 11; 9, 29, 31, 11; 9, 38, 60, 42, 11; 9, 47, 98, 102, 53, 11; 9, 56, 145, 200, 155, 64, 11; 9, 65, 201, 345, 355, 219, 75, 11; 9, 74, 266, 546, 700, 574, 294, 86, 11; 9, 83, 340, 812, 1246, 1274, 868, 380, 97, 11; 9, 92, 423, 1152, 2058, 2520, 2142, 1248, 477, 108, 11; MATHEMATICA T[n_, k_]:= If[n==0, 1, (9 + 2*k/n)*Binomial[n, k]] Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Apr 28 2022 *) PROG (SageMath) def A172185(n, k): return 9*binomial(n, k) +2*binomial(n-1, k-1) -8*bool(n==0) flatten([[A172185(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 28 2022 CROSSREFS Cf. A022114, A093644, A172179. Sequence in context: A266703 A266701 A172283 * A098728 A233408 A107576 Adjacent sequences: A172182 A172183 A172184 * A172186 A172187 A172188 KEYWORD nonn,tabl AUTHOR Mark Dols, Jan 28 2010 EXTENSIONS Corrected and extended by Philippe Deléham, Oct 09 2011 STATUS approved

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Last modified June 2 17:31 EDT 2023. Contains 363100 sequences. (Running on oeis4.)