A053739 Partial sums of A014166.

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

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