A373302 - OEIS

%I #37 Jun 24 2024 08:46:57

%S 1,6,27,119,533,2402,10829,48804,219925,991044,4465957,20125051,

%T 90690002,408678475,1841637299,8299012941,37398034921,168527634148,

%U 759439995404,3422282105232,15421909405056,69496108849357,313171930813206,1411253951813003,6359566489040219

%N Number of compositions of 6*n-2 into parts 1 and 6.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (7,-15,20,-15,6,-1).

%F a(n) = A005708(6*n-2).

%F a(n) = Sum_{k=0..n} binomial(n+3+5*k,n-1-k).

%F a(n) = 7*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

%F G.f.: x*(1-x)/((1-x)^6 - x).

%F a(n) = A099242(n-1) - A099242(n-2).

%o (PARI) a(n) = sum(k=0, n, binomial(n+3+5*k, n-1-k));

%Y Cf. A099242, A371125, A373958, A373959, A373960.

%Y Cf. A005708, A373928.

%K nonn,easy

%O 1,2

%A _Seiichi Manyama_, Jun 23 2024