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A094866
Number of truncated ST-pairs O(q^n).
0
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.
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
KEYWORD
nonn
AUTHOR
Barry Cipra, Jun 15 2004
STATUS
approved