A373913 - OEIS

%I #14 Jul 29 2024 11:08:30

%S 1,1,1,1,1,1,1,2,10,46,166,496,1288,3004,6437,12888,24464,44728,80428,

%T 146320,278104,564929,1225811,2778772,6396236,14620646,32760586,

%U 71565796,152344397,316911454,647536777,1308456096,2635130392,5330198752,10896635912

%N Number of compositions of 8*n into parts 7 and 8.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,9,-1).

%F a(n) = A017857(8*n).

%F a(n) = Sum_{k=0..floor(n/7)} binomial(n+k,n-7*k).

%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 9*a(n-7) - a(n-8).

%F G.f.: 1/(1 - x - x^7/(1 - x)^7).

%t CoefficientList[Series[1/(1-x-x^7/(1-x)^7),{x,0,40}],x] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,9,-1},{1,1,1,1,1,1,1,2},40] (* _Harvey P. Dale_, Jul 29 2024 *)

%o (PARI) a(n) = sum(k=0, n\7, binomial(n+k, n-7*k));

%Y Cf. A099099, A099131, A107025, A373912.

%Y Cf. A017857.

%K nonn,easy

%O 0,8

%A _Seiichi Manyama_, Jun 22 2024