OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Kelsey Blum, Bounds on the Number of Graphical Partitions, arXiv:2103.03196 [math.CO], 2021. See Table on p. 7. [Given a(10) is incorrect.]
FORMULA
PROG
(PARI) \\ by partitions
a(n)={my(total=0); forpart(q=2*n, my(p=Vecrev(q), m=0, s=0); while(m<#p && p[m+1]>m, m++; s+=p[m]-m); if(s + m <= n, total++) ); total} \\ Andrew Howroyd, Jan 03 2024
(PARI) \\ faster version using g.f.'s
a(n)=sum(m=1, sqrtint(2*n), my(r=2*n-m^2); my(g=1/prod(k=1, m, 1 - x^k + O(x*x^r))); sum(i=0, n-binomial(m+1, 2), polcoef(g, i)*polcoef(g, r-i)) ) \\ Andrew Howroyd, Jan 03 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Mar 05 2021
EXTENSIONS
Corrected and extended by Andrew Howroyd, Jan 03 2024
STATUS
approved