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 A053739 Partial sums of A014166. 10
 1, 6, 22, 63, 155, 344, 709, 1383, 2587, 4685, 8273, 14323, 24416, 41119, 68595, 113590, 187030, 306605, 500950, 816410, 1327986, 2157046, 3499982, 5674578, 9195035, 14893364, 24115804, 39040633, 63192397, 102273950, 165512723, 267839033, 433410661, 701315739, 1134800215 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 Hung Viet Chu, Partial Sums of the Fibonacci Sequence, arXiv:2106.03659 [math.CO], 2021. Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1). FORMULA a(n) = Sum_{i=0..floor(n/2)} binomial(n+5-i, n-2*i) for n >= 0. a(n) = a(n-1) + a(n-2) + C(n+4,4); n >= 0; a(-1)=0. G.f.: 1/((1-x-x^2)*(1-x)^5). - R. J. Mathar, May 22 2013 a(n) = Fibonacci(n+11) - (n^4 + 22*n^3 + 203*n^2 + 974*n + 2112)/4!. - G. C. Greubel, Sep 06 2019 MAPLE with(combinat); seq(fibonacci(n+11)-(n^4 + 22*n^3 + 203*n^2 + 974*n + 2112)/4!, n = 0..35); # G. C. Greubel, Sep 06 2019 MATHEMATICA Table[Fibonacci[n+11] -(n^4+22*n^3+203*n^2+974*n+2112)/4!, {n, 0, 35}] (* G. C. Greubel, Sep 06 2019 *) PROG (PARI) vector(35, n, m=n-1; fibonacci(n+10) - (m^4+22*m^3+203*m^2+974*m +2112)/4!) \\ G. C. Greubel, Sep 06 2019 (Magma) [Fibonacci(n+11) - (n^4+22*n^3+203*n^2+974*n+2112)/24: n in [0..35]]; // G. C. Greubel, Sep 06 2019 (Sage) [fibonacci(n+11) - (n^4+22*n^3+203*n^2+974*n+2112)/24 for n in (0..35)] # G. C. Greubel, Sep 06 2019 (GAP) List([0..35], n-> Fibonacci(n+11)-(n^4+22*n^3+203*n^2+974*n + 2112)/24); # G. C. Greubel, Sep 06 2019 CROSSREFS Cf. A014166 and A000045. Right-hand column 10 of triangle A011794. Cf. A228074. Sequence in context: A257200 A258474 A120477 * A280481 A055797 A001925 Adjacent sequences: A053736 A053737 A053738 * A053740 A053741 A053742 KEYWORD easy,nonn AUTHOR Barry E. Williams, Feb 13 2000 EXTENSIONS Terms a(28) onward added by G. C. Greubel, Sep 06 2019 STATUS approved

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Last modified April 24 18:17 EDT 2024. Contains 371962 sequences. (Running on oeis4.)