A363936 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.

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

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Formula

a(n) <= A000569(n).

Maple

K:=1
product((1+z*q*q^j)^k*(1+z^-1*x^j)^k, j=0..40):
series(%, q, 35):
convert(%, polynom):
expand(%):
A:=coeff(%, z, 0):
for m from 2 by 2 to 40 do
for i to m do f(m):=add(coeff(coeff(A, x, i), q, m-i), i=m/2..m);
end do;
for n from 2 by 2 to 40 do
a(n):=f(n)-coeff(coeff(A, q, n/2), x, n/2); end do

Crossrefs

Cf. A000569.

Sequence in context: A241564 A135348 A305101 * A083322 A073939 A085264

Adjacent sequences: A363933 A363934 A363935 * A363937 A363938 A363939

Keyword

nonn,more

Author

Kelsey A. Blum, Jul 09 2023

Status

approved