OFFSET
1,5
LINKS
John Tyler Rascoe, Table of n, a(n) for n = 1..200
FORMULA
G.f.: Sum_{i>0} Sum_{j>0} x^(3*i+j) /Product_{k=i..2*i+j} (1 - x^k). - John Tyler Rascoe, Jun 21 2025
EXAMPLE
a(6) = 4 counts these partitions: 51, 411, 321, 3111.
MATHEMATICA
z = 60; q[n_] := q[n] = IntegerPartitions[n];
Table[Count[q[n], p_ /; 2 Min[p] < Max[p]], {n, z}] (* A237820 *)
Table[Count[q[n], p_ /; 2 Min[p] <= Max[p]], {n, z}] (* A237821 *)
Table[Count[q[n], p_ /; 2 Min[p] = = Max[p]], {n, z}](* A118096 *)
Table[Count[q[n], p_ /; 2 Min[p] > Max[p]], {n, z}] (* A053263 *)
Table[Count[q[n], p_ /; 2 Min[p] >= Max[p]], {n, z}] (* A237824 *)
PROG
(PARI) A(n) = {concat([0, 0, 0], Vec(sum(i=1, n, sum(j=1, n-3*i, x^(3*i+j)/prod(k=i, min(n-3*i-j, 2*i+j), 1-x^k)))+ O('x^(n+1))))} \\ John Tyler Rascoe, Jun 21 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 16 2014
STATUS
approved
