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 A134465 Row sums of triangle A134464. 4
 1, 6, 16, 32, 55, 86, 126, 176, 237, 310, 396, 496, 611, 742, 890, 1056, 1241, 1446, 1672, 1920, 2191, 2486, 2806, 3152, 3525, 3926, 4356, 4816, 5307, 5830, 6386, 6976, 7601, 8262, 8960, 9696, 10471, 11286, 12142, 13040, 13981, 14966 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of compositions of n+9 into n parts avoiding parts 2 and 3. - Milan Janjic, Jan 07 2016 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 David Anderson, E. S. Egge, M. Riehl, L. Ryan, R. Steinke, Y. Vaughan, Pattern Avoiding Linear Extensions of Rectangular Posets, arXiv:1605.06825 [math.CO], 2016. Colin Defant, Proofs of Conjectures about Pattern-Avoiding Linear Extensions, arXiv:1905.02309 [math.CO], 2019. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA Binomial transform of [1, 5, 5, 1, 0, 0, 0, ...]. G.f.: x*(1+2*x-2*x^2) / (1-x)^4. - R. J. Mathar, Apr 04 2012 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 29 2012 EXAMPLE a(4) = 32 = sum of row 4, triangle A134464: (4 + 6 + 9 + 13). a(4) = 32 = (1, 3, 3, 1) dot (1, 5, 5, 1) = (1 + 15 + 15 + 1). MATHEMATICA CoefficientList[Series[(1+2*x-2*x^2)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 29 2012 *) PROG (Magma) I:=[1, 6, 16, 32]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012 (PARI) Vec(x*(1+2*x-2*x^2)/(1-x)^4 + O(x^50)) \\ Altug Alkan, Jan 07 2016 (Sage) ((1+2*x-2*x^2)/(1-x)^4).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, May 08 2019 (GAP) a:=[1, 6, 16, 32];; for n in [5..50] do a[n]:=4*a[n-1]-6*a[n-2]+ 4*a[n-3]-a[n-4]; od; a; # G. C. Greubel, May 08 2019 CROSSREFS Cf. A134464. Sequence in context: A341276 A301698 A301713 * A036488 A131949 A345023 Adjacent sequences: A134462 A134463 A134464 * A134466 A134467 A134468 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Oct 26 2007 STATUS approved

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Last modified September 18 21:47 EDT 2024. Contains 376002 sequences. (Running on oeis4.)