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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
0, 1, 2, 6, 11, 22, 40, 72, 120, 203, 331, 526, 828, 1277, 1947, 2931, 4372
OFFSET
1,3
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
KEYWORD
nonn,more
AUTHOR
Kelsey A. Blum, Jul 09 2023
STATUS
approved