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A053809
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Second partial sums of A001891.
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2
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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
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listen;
history;
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OFFSET
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0,2
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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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
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MATHEMATICA
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Table[Fibonacci[n+10] - (2*n^3+27*n^2+145*n+324)/6, {n, 0, 40}] (* G. C. Greubel, Jul 06 2019 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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