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Number of compositions of 7*n-2 into parts 6 and 7.
4

%I #15 Jun 24 2024 05:41:34

%S 0,1,3,6,10,15,21,29,46,100,275,781,2080,5097,11562,24583,49725,97376,

%T 188480,368734,742811,1553192,3353332,7372536,16261025,35583926,

%U 76806997,163327279,342902007,713848316,1481274767,3078928619,6433465844,13534471164

%N Number of compositions of 7*n-2 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-2).

%F a(n) = Sum_{k=0..floor(n/6)} binomial(n+k,n-2-6*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^2*(1-x)^4/((1-x)^7 - x^6).

%F a(n) = A373935(n+1)-A373935(n). - _R. J. Mathar_, Jun 24 2024

%o (PARI) a(n) = sum(k=0, n\6, binomial(n+k, n-2-6*k));

%Y Cf. A369809, A373912, A373933, A373935, A373936, A373937.

%Y Cf. A017847, A369850.

%K nonn,easy

%O 1,3

%A _Seiichi Manyama_, Jun 23 2024