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%I #20 Sep 08 2022 08:45:00
%S 1,6,21,57,133,281,554,1039,1878,3302,5686,9638,16143,26796,44179,
%T 72471,118435,193015,313920,509805,827036,1340636,2171996,3517532,
%U 5695053,9218786,14920769,24147269,39076593,63233317,102320326
%N Second partial sums of A001891.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H G. C. Greubel, <a href="/A053809/b053809.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,6,1,-3,1).
%F a(n) = a(n-1) + a(n-2) + (2*n+3)*C(n+2, 2)/3; a(-x)=0.
%F a(n) = Fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6.
%F G.f.: (1+x)/((1-x)^4*(1-x-x^2)).
%F 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
%t Table[Fibonacci[n+10] - (2*n^3+27*n^2+145*n+324)/6, {n,0,40}] (* _G. C. Greubel_, Jul 06 2019 *)
%o (PARI) vector(40, n, n--; fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6) \\ _G. C. Greubel_, Jul 06 2019
%o (Magma) [Fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6: n in [0..40]]; // _G. C. Greubel_, Jul 06 2019
%o (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
%o (GAP) List([0..40], n-> Fibonacci(n+10) - (2*n^3 + 27*n^2 + 145*n + 324)/6) # _G. C. Greubel_, Jul 06 2019
%Y Cf. A001911, A001891, A053808.
%Y Right-hand column 9 of triangle A011794. Pairwise sums of A014166.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Mar 27 2000
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