A363936 - OEIS

%I #118 Aug 02 2023 14:31:59

%S 0,1,2,6,11,22,40,72,120,203,331,526,828,1277,1947,2931,4372

%N Number of Frobenius partitions of 2n wherein the number of columns plus the weight on the top row is strictly less than the weight on the bottom row.

%F a(n) <= A000569(n).

%p K:=1

%p product((1+z*q*q^j)^k*(1+z^-1*x^j)^k, j=0..40):

%p series(%,q,35):

%p convert(%,polynom):

%p expand(%):

%p A:=coeff(%,z,0):

%p for m from 2 by 2 to 40 do

%p for i to m do f(m):=add(coeff(coeff(A,x,i),q,m-i),i=m/2..m);

%p end do;

%p for n from 2 by 2 to 40 do

%p a(n):=f(n)-coeff(coeff(A,q,n/2),x,n/2); end do

%Y Cf. A000569.

%K nonn,more

%O 1,3

%A _Kelsey A. Blum_, Jul 09 2023