A369813 - OEIS

%I #20 Dec 04 2024 14:56:58

%S 1,0,1,0,1,0,1,1,1,2,1,3,1,4,2,5,4,6,7,7,11,9,16,13,22,20,29,31,38,47,

%T 51,69,71,98,102,136,149,187,218,258,316,360,452,509,639,727,897,1043,

%U 1257,1495,1766,2134,2493,3031,3536,4288,5031,6054,7165,8547,10196,12083,14484,17114,20538,24279,29085,34475

%N Expansion of 1/(1 - x^2 - x^7).

%C Number of compositions of n into parts 2 and 7.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,1).

%F a(n) = a(n-2) + a(n-7).

%F a(n) = A007380(n-7) for n >= 8.

%t CoefficientList[Series[1/(1-x^2-x^7),{x,0,80}],x] (* or *) LinearRecurrence[{0,1,0,0,0,0,1},{1,0,1,0,1,0,1},80] (* _Harvey P. Dale_, Dec 04 2024 *)

%o (PARI) my(N=70, x='x+O('x^N)); Vec(1/(1-x^2-x^7))

%o (PARI) a(n) = sum(k=0, n\7, ((n-5*k)%2==0)*binomial((n-5*k)/2, k));

%Y Cf. A005709, A017847, A369814, A369815, A369816.

%Y Cf. A007380.

%K nonn,easy

%O 0,10

%A _Seiichi Manyama_, Feb 02 2024