Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #13 Jun 24 2024 05:43:14
%S 0,0,1,4,10,20,35,56,85,131,231,506,1287,3367,8464,20026,44609,94334,
%T 191710,380190,748924,1491735,3044927,6398259,13770795,30031820,
%U 65615746,142422743,305750022,648652029,1362500345,2843775112,5922703731,12356169575
%N Number of compositions of 7*n-3 into parts 6 and 7.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-6,1).
%F a(n) = A017847(7*n-3).
%F a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-3-6*k).
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 6*a(n-6) + a(n-7).
%F G.f.: x^3*(1-x)^3/((1-x)^7 - x^6).
%F a(n) = A373936(n+1)-A373936(n). - _R. J. Mathar_, Jun 24 2024
%o (PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-3-6*k));
%Y Cf. A369809, A373912, A373933, A373934, A373936, A373937.
%Y Cf. A017847.
%K nonn,easy
%O 1,4
%A _Seiichi Manyama_, Jun 23 2024