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 A274772 Zero together with the partial sums of A056640. 1
 0, 1, 6, 24, 66, 149, 292, 520, 860, 1345, 2010, 2896, 4046, 5509, 7336, 9584, 12312, 15585, 19470, 24040, 29370, 35541, 42636, 50744, 59956, 70369, 82082, 95200, 109830, 126085, 144080, 163936, 185776, 209729, 235926, 264504, 295602, 329365, 365940, 405480, 448140, 494081, 543466, 596464, 653246, 713989, 778872, 848080, 921800, 1000225, 1083550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS I LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1). FORMULA a(n) = (4*n^4+8*n^3+2*n^2+4*n+3*(1-(-1)^n))/24. Therefore : a(2*k) = k*(k+1)*(8*k^2+1)/3, a(2*k+1) = (k+1)*(8*k^3+16*k^2+9*k+3)/3. From Colin Barker, Nov 11 2016: (Start) G.f.: x*(1 + 2*x + 5*x^2) / ((1 - x)^5 * (1 + x)). a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6) for n>5. (End) EXAMPLE a(0) = 0, a(1) = 1, a(2) = 6, a(3) = 24, a(4) = 66. MATHEMATICA LinearRecurrence[{4, -5, 0, 5, -4, 1}, {0, 1, 6, 24, 66, 149}, 60] (* Harvey P. Dale, Jun 19 2021 *) PROG (PARI) concat(0, Vec(x*(1 + 2*x + 5*x^2) / ((1 - x)^5 * (1 + x)) + O(x^50))) \\ Colin Barker, Nov 11 2016 CROSSREFS Cf. A001844, A005900, A056640. Sequence in context: A101877 A270851 A092348 * A369177 A234271 A338512 Adjacent sequences: A274769 A274770 A274771 * A274773 A274774 A274775 KEYWORD nonn,easy AUTHOR Luce ETIENNE, Nov 11 2016 STATUS approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)