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%I #41 Dec 30 2023 23:48:33
%S 1,8,37,129,376,967,2267,4950,10220,20175,38403,70954,127921,226007,
%T 392688,672959,1140260,1914166,3189022,5280288,8699540,14275838,
%U 23352118,38102976,62048869,100888126,163843187,265838881,431026972,698489013,1131463777,1832277574,2966502032,4802042229
%N Partial sums of A053295.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
%H G. C. Greubel, <a href="/A053296/b053296.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (8,-27,49,-49,21,7,-13,6,-1).
%F a(n) = Sum_{i=0..floor(n/2)} C(n+7-i, n-2i), n >= 0.
%F a(n) = a(n-1) + a(n-2) + C(n+6,6); n >= 0; a(-1)=0.
%t Table[Sum[Binomial[n+7-j, n-2*j], {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+7-j, n-2*j)), ", ")) \\ _G. C. Greubel_, May 24 2018
%o (Magma) [(&+[Binomial(n+7-j, n-2*j): j in [0..Floor(n/2)]]): n in [0..30]]; // _G. C. Greubel_, May 24 2018
%Y Cf. A053739, A014166 and A136431.
%Y Right-hand column 14 of triangle A011794.
%Y Cf. A228074.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Mar 04 2000
%E Terms a(28) onward added by _G. C. Greubel_, May 24 2018
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