A094866 Number of truncated ST-pairs O(q^n).

1, 2, 4, 6, 11, 15, 26, 41, 67, 96, 138, 197, 300, 431, 636, 893, 1258, 1723, 2447, 3425, 4962, 6839, 10000, 13989, 21383, 30781, 48292, 70456, 110214, 159686, 253265, 374385, 591648, 876405, 1354888

Offset

3,2

Comments

A truncated ST-pair O(q^n) consists of a subset S of {1, 2, ..., n-1} and a subset T of {1, 2, ..., n-2} such that (Product_{k in S} 1/(1-q^k)) - q (Product_{k in T} 1/(1-q^k)) = 1 + O(q^n). - Andrey Zabolotskiy, Feb 27 2024

References

F. G. Garvan, Shifted and Shiftless Partition Identities, in Number Theory for the Millennium II (M. A. Bennett et al., eds.), AK Peters, Ltd. 2002, pp. 75-92.

Links

Table of n, a(n) for n=3..37.

F. G. Garvan, Shifted and shiftless partition identities (2001).

Mathematica

st[n_] := Select[Flatten[Table[{s, t}, {s, Subsets@Range[n - 1]}, {t, Subsets@Range[n - 2]}], 1], Normal[Product[1/(1-q^k) + O[q]^n, {k, First@#}] - q Product[1/(1-q^k) + O[q]^n, {k, Last@#}] - 1] == 0 &];
Table[Length@st[n], {n, 3, 9}] (* Andrey Zabolotskiy, Feb 27 2024 *)

Crossrefs

Sequence in context: A187492 A366127 A103580 * A072951 A325591 A062766

Adjacent sequences: A094863 A094864 A094865 * A094867 A094868 A094869

Keyword

nonn

Author

Barry Cipra, Jun 15 2004

Status

approved