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 A070832 a(n) = Sum_{k=0..n} binomial(8*n,8*k). 10
 1, 2, 12872, 1470944, 622116992, 125858012672, 36758056208384, 8793364151263232, 2334899414608412672, 586347560750962049024, 151652224498623981289472, 38612725801339748322639872, 9913426188311626771400228864 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..415 Index entries for linear recurrences with constant coefficients, signature (136,32880,-552704,-65536). FORMULA Let b(n) = a(n)-2^(8*n)/8 then b(n)+120*b(n-1)-2160*b(n-2)-256*b(n-3)=0. - Benoit Cloitre, May 27 2004 a(n) = 1/4*16^n + 1/8*256^n + 1/4*(-68 + 48*sqrt(2))^n + 1/4*(-68-48*sqrt(2))^n. From Colin Barker, May 27 2019: (Start) G.f.: (1 - 134*x - 20280*x^2 + 207296*x^3 + 8192*x^4) / ((1 - 16*x)*(1 - 256*x)*(1 + 136*x + 16*x^2)). a(n) = 21*a(n-1) + 353*a(n-2) - 32*a(n-3) for n>4. (End) MATHEMATICA Table[Sum[Binomial[8n, 8k], {k, 0, n}], {n, 0, 15}] (* Harvey P. Dale, Nov 25 2020 *) PROG (PARI) a(n)=sum(k=0, n, binomial(8*n, 8*k)); \\ Benoit Cloitre, May 27 2004 (PARI) Vec((1 - 134*x - 20280*x^2 + 207296*x^3 + 8192*x^4) / ((1 - 16*x)*(1 - 256*x)*(1 + 136*x + 16*x^2)) + O(x^15)) \\ Colin Barker, May 27 2019 CROSSREFS Sum_{k=0..n} binomial(b*n,b*k): A000079 (b=1), A081294 (b=2), A007613 (b=3), A070775 (b=4), A070782 (b=5), A070967 (b=6), A094211 (b=7), this sequence (b=8), A094213 (b=9), A070833 (b=10). Sequence in context: A265013 A083973 A094212 * A170994 A151599 A297573 Adjacent sequences: A070829 A070830 A070831 * A070833 A070834 A070835 KEYWORD easy,nonn AUTHOR Sebastian Gutierrez and Sarah Kolitz (skolitz(AT)mit.edu), May 15 2002 EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007 STATUS approved

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Last modified September 19 14:36 EDT 2024. Contains 376012 sequences. (Running on oeis4.)