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 A053808 Partial sums of A001891. 12
 1, 5, 15, 36, 76, 148, 273, 485, 839, 1424, 2384, 3952, 6505, 10653, 17383, 28292, 45964, 74580, 120905, 195885, 317231, 513600, 831360, 1345536, 2177521, 3523733, 5701983, 9226500, 14929324, 24156724, 39087009, 63244757, 102332855, 165578768, 267912848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Antidiagonal sums of the convolution array A213579 and row 1 of the convolution array A213590. - Clark Kimberling, Jun 18 2012 Also number CG(n,2) of complete games with n players of 2 types. - N. J. A. Sloane, Dec 29 2012 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 J. Freixas and S. Kurz, The golden number and Fibonacci sequences in the design of voting structures, 2012. - From N. J. A. Sloane, Dec 29 2012 W. Lang, Problem B-858, Fibonacci Quarterly, 36,3 (1998) 373-374; Solution, ibid. 37,2 (1999) 183-184. Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1). FORMULA a(n) = a(n-1) + a(n-2) + (n+1)^2, a(-n)=0. G.f.: (1+x)/((1-x-x^2)*(1-x)^3). a(n) = Fibonacci(n+6) - (n^2 + 4*n + 8), n >= 2 (see p. 184 of FQ reference). a(n-2) = Sum_{i=0..n} Fibonacci(i)*(n-i)^2. - Benoit Cloitre, Mar 06 2004 MATHEMATICA Table[Fibonacci[n+8] -(n^2 +8*n+20), {n, 0, 40}] (* G. C. Greubel, Jul 06 2019 *) PROG (PARI) vector(40, n, n--; fibonacci(n+8) - (n^2 +8*n+20)) \\ G. C. Greubel, Jul 06 2019 (MAGMA) [Fibonacci(n+8) - (n^2+8*n+20): n in [0..40]]; // G. C. Greubel, Jul 06 2019 (Sage) [fibonacci(n+8) - (n^2 +8*n+20) for n in (0..20)] # G. C. Greubel, Jul 06 2019 (GAP) List([0..40], n-> Fibonacci(n+8) - (n^2 +8*n+20)) # G. C. Greubel, Jul 06 2019 CROSSREFS Convolution of A000290 (squares) with A000045, n >= 1. (Fibonacci) - Wolfdieter Lang, Apr 10 2000 Right-hand column 7 of triangle A011794. Sequence in context: A046776 A144898 A163250 * A111926 A137609 A109818 Adjacent sequences:  A053805 A053806 A053807 * A053809 A053810 A053811 KEYWORD easy,nonn AUTHOR Barry E. Williams, Mar 27 2000 STATUS approved

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Last modified February 26 02:19 EST 2020. Contains 332270 sequences. (Running on oeis4.)