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 A073379 Ninth convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0, with itself. 2
 1, 10, 75, 440, 2255, 10362, 43945, 174460, 656370, 2359500, 8158722, 27275040, 88524930, 279892380, 864508590, 2614740216, 7759693095, 22634343270, 64990287285, 183929970840, 513661549401, 1416970676550 (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 (10,-25,-60,330,12,-1770,960,5835,-4070,-13597, 8140,23340,-7680,-28320,-384,21120,7680,-6400,-5120,-1024). FORMULA a(n) = Sum_{k=0..n} (b(k)*c(n-k), with b(k) = A001045(k+1) and c(k) = A073378(k). a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9) * binomial(n-k, k) * 2^k. G.f.: 1/(1-(1+2*x)*x)^10 = 1/((1+x)*(1-2*x))^10. MATHEMATICA CoefficientList[Series[1/((1+x)*(1-2*x))^10, {x, 0, 40}], x] (* G. C. Greubel, Oct 01 2022 *) PROG (Magma) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^10 )); // G. C. Greubel, Oct 01 2022 (SageMath) def A073379_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( 1/((1+x)*(1-2*x))^10 ).list() A073379_list(40) # G. C. Greubel, Oct 01 2022 CROSSREFS Tenth (m=9) column of triangle A073370. Cf. A001045, A073370, A073378, A073399, A073400. Sequence in context: A026969 A026979 A274251 * A283238 A316462 A022734 Adjacent sequences: A073376 A073377 A073378 * A073380 A073381 A073382 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Aug 02 2002 STATUS approved

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Last modified July 15 10:33 EDT 2024. Contains 374332 sequences. (Running on oeis4.)