A053809 Second partial sums of A001891.

1, 6, 21, 57, 133, 281, 554, 1039, 1878, 3302, 5686, 9638, 16143, 26796, 44179, 72471, 118435, 193015, 313920, 509805, 827036, 1340636, 2171996, 3517532, 5695053, 9218786, 14920769, 24147269, 39076593, 63233317, 102320326

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

Index entries for linear recurrences with constant coefficients, signature (5,-9,6,1,-3,1).

Formula

a(n) = a(n-1) + a(n-2) + (2*n+3)*C(n+2, 2)/3; a(-x)=0.

a(n) = Fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6.

G.f.: (1+x)/((1-x)^4*(1-x-x^2)).

a(n) = 5*a(n-1) - 9*a(n-2) + 6*a(n-3) + a(n-4) - 3*a(n-5) + a(n-6). - Wesley Ivan Hurt, Apr 21 2021

Mathematica

Table[Fibonacci[n+10] - (2*n^3+27*n^2+145*n+324)/6, {n, 0, 40}] (* G. C. Greubel, Jul 06 2019 *)

Prog

(PARI) vector(40, n, n--; fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6) \\ G. C. Greubel, Jul 06 2019
(Magma) [Fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6: n in [0..40]]; // G. C. Greubel, Jul 06 2019
(Sage) [fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6 for n in (0..40)] # G. C. Greubel, Jul 06 2019
(GAP) List([0..40], n-> Fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6) # G. C. Greubel, Jul 06 2019

Crossrefs

Cf. A001911, A001891, A053808.

Right-hand column 9 of triangle A011794. Pairwise sums of A014166.

Sequence in context: A056414 A056341 A144899 * A381265 A290891 A047520

Adjacent sequences: A053806 A053807 A053808 * A053810 A053811 A053812

Keyword

easy,nonn

Author

Barry E. Williams, Mar 27 2000

Status

approved