cp's OEIS Frontend

A380121 a(n) = C(n, Q(n+3, 4)-1)*C(n, Q(n+1, 4)) + C(n, Q(3*n+1, 4))*C(n, Q(3*n+3, 4)) where C = binomial and Q(x, y) = floor(x/y).

%I A380121 #8 Jan 19 2025 07:38:45
%S A380121 1,2,3,6,20,50,126,294,1008,2592,7425,18150,62920,163592,496860,
%T A380121 1242150,4331600,11328800,35581680,90140256,315490896,828163602,
%U A380121 2658338298,6793531206,23836951600,62728820000,204451146900,525731520600,1848025951200,4872068416800,16059866355000
%N A380121 a(n) = C(n, Q(n+3, 4)-1)*C(n, Q(n+1, 4)) + C(n, Q(3*n+1, 4))*C(n, Q(3*n+3, 4)) where C = binomial and Q(x, y) = floor(x/y).
%C A380121 a(n) is the minimum of row n of A378067 except at n = 1.
%p A380121 a := n -> binomial(n, iquo(n+3, 4)-1) * binomial(n, iquo(n+1, 4)) + binomial(n, iquo(3*n+1, 4)) * binomial(n,iquo(3*n+3, 4)): seq(a(n), n = 0..29);
%o A380121 (Python)
%o A380121 from math import comb as C
%o A380121 def a(n): return C(n,(n+3)//4-1)*C(n,(n+1)//4)+C(n,(3*n+1)//4)*C(n,(3*n+3)//4) if n>0 else 1; print([a(n) for n in range(31)])
%Y A380121 Cf. A378067.
%K A380121 nonn
%O A380121 0,2
%A A380121 _Peter Luschny_, Jan 17 2025