%I #11 Jun 22 2024 14:11:51

%S 1,1,1,2,9,37,122,346,913,2398,6515,18317,52226,148408,417810,1168085,

%T 3258813,9103828,25488736,71462437,200406479,561770980,1573939555,

%U 4408629727,12348599802,34592601763,96916209910,271537125048,760777555986,2131439888257

%N Number of compositions of 7*n into parts 3 and 7.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,36,-35,21,-7,1).

%F a(n) = A369814(7*n).

%F a(n) = Sum_{k=0..floor(n/3)} binomial(n+4*k,n-3*k).

%F a(n) = 7*a(n-1) - 21*a(n-2) + 36*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

%F G.f.: 1/(1 - x - x^3/(1 - x)^6).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n+4*k, n-3*k));

%Y Cf. A373907, A373908, A373910, A373911, A373912.

%Y Cf. A369814.

%K nonn,easy

%O 0,4

%A _Seiichi Manyama_, Jun 22 2024