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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 (list; graph; refs; listen; history; text; internal format)
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
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

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)