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 A289721 Let a(0)=1. Then a(n) = sums of consecutive strings of positive integers of length 3*n, starting with the integer 2. 1
 1, 9, 45, 135, 306, 585, 999, 1575, 2340, 3321, 4545, 6039, 7830, 9945, 12411, 15255, 18504, 22185, 26325, 30951, 36090, 41769, 48015, 54855, 62316, 70425, 79209, 88695, 98910, 109881, 121635, 134199, 147600, 161865, 177021, 193095, 210114, 228105, 247095, 267111, 288180 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA From Colin Barker, Aug 14 2017: (Start) G.f.: (1 + 5*x + 15*x^2 + 5*x^3 + x^4) / (1 - x)^4. a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4. (End) EXAMPLE 1, 2 + 3 + 4, 5 + 6 + 7 + 8 + 9 + 10, ... MATHEMATICA CoefficientList[Series[(1 + 5 x + 15 x^2 + 5 x^3 + x^4)/(1 - x)^4, {x, 0, 40}], x] (* Michael De Vlieger, Aug 15 2017 *) PROG (PARI) Vec((1 + 5*x + 15*x^2 + 5*x^3 + x^4) / (1 - x)^4 + O(x^100)) \\ Colin Barker, Aug 14 2017 CROSSREFS Sequence in context: A152996 A188351 A220443 * A060008 A212089 A212142 Adjacent sequences: A289718 A289719 A289720 * A289722 A289723 A289724 KEYWORD nonn,easy AUTHOR Enrique Navarrete, Aug 13 2017 STATUS approved

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Last modified March 2 21:56 EST 2024. Contains 370498 sequences. (Running on oeis4.)