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A053809 Second partial sums of A001891. 2
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 (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

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)).

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 * A290891 A047520 A294836

Adjacent sequences:  A053806 A053807 A053808 * A053810 A053811 A053812

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Mar 27 2000

STATUS

approved

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Last modified April 7 12:45 EDT 2020. Contains 333305 sequences. (Running on oeis4.)