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 A073378 Eighth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself. 3
 1, 9, 63, 345, 1665, 7227, 29073, 109791, 394020, 1354210, 4486482, 14397318, 44932446, 136817370, 407566350, 1190446866, 3415935699, 9645169743, 26836557825, 73670997015, 199751003991, 535449185469 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For a(n) in terms of U(n+1) and U(n) with U(n) = A001045(n+1) see A073370 and the row polynomials of triangles A073399 and A073400. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-18,-60,234,126,-1176,36,3519,-479,-7038,144, 9408,2016,-7488,-3840,2304,2304,512). FORMULA a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073377(k). a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+8, 8) * binomial(n-k, k) * 2^k. G.f.: 1/(1-(1+2*x)*x)^9 = 1/((1+x)*(1-2*x))^9. MATHEMATICA CoefficientList[Series[1/((1+x)*(1-2*x))^9, {x, 0, 40}], x] (* G. C. Greubel, Oct 01 2022 *) PROG (Magma) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^9 )); // G. C. Greubel, Oct 01 2022 (SageMath) def A073378_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( 1/((1+x)*(1-2*x))^9 ).list() A073378_list(40) # G. C. Greubel, Oct 01 2022 CROSSREFS Ninth (m=8) column of triangle A073370. Cf. A001045, A073377, A073399, A073400, A073401. Sequence in context: A178161 A015669 A202982 * A316461 A022733 A111997 Adjacent sequences: A073375 A073376 A073377 * A073379 A073380 A073381 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 02 2002 STATUS approved

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Last modified June 8 00:26 EDT 2023. Contains 363157 sequences. (Running on oeis4.)