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%I #36 Dec 30 2023 23:48:37
%S 1,9,46,175,551,1518,3785,8735,18955,39130,77533,148487,276408,502415,
%T 895103,1568062,2708322,4622488,7811510,13091798,21791338,36067176,
%U 59419294,97522270,159571139,260459265,424302452,690141333
%N Partial sums of A053296.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
%H G. C. Greubel, <a href="/A053308/b053308.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (9,-35,76,-98,70,-14,-20,19,-7,1).
%F a(n) = Sum_{i=0..floor(n/2)} C(n+8-i, n-2i), n >= 0.
%F a(n) = a(n-1) + a(n-2) + C(n+7,7); n >= 0; a(-1)=0.
%t Table[Sum[Binomial[n+8-j, n-2j], {j, 0, Floor[n/2]}], {n, 0, 50}] (* _G. C. Greubel_, May 24 2018 *)
%o (PARI) for(n=0, 30, print1(sum(j=0, floor(n/2), binomial(n+8-j, n-2*j)), ", ")) \\ _G. C. Greubel_, May 24 2018
%o (Magma) [(&+[Binomial(n+8-j, n-2*j): j in [0..Floor(n/2)]]): n in [0..30]]; // _G. C. Greubel_, May 24 2018
%Y Cf. A053296, A053295, A136431.
%Y Cf. A228074.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Mar 06 2000
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