A094866 - OEIS

%I #16 Feb 27 2024 14:43:35

%S 1,2,4,6,11,15,26,41,67,96,138,197,300,431,636,893,1258,1723,2447,

%T 3425,4962,6839,10000,13989,21383,30781,48292,70456,110214,159686,

%U 253265,374385,591648,876405,1354888

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

%C 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

%D 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.

%H F. G. Garvan, <a href="https://qseries.org/fgarvan/publist.html#shifted">Shifted and shiftless partition identities</a> (2001).

%t 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 &];

%t Table[Length@st[n], {n, 3, 9}] (* _Andrey Zabolotskiy_, Feb 27 2024 *)

%K nonn

%O 3,2

%A _Barry Cipra_, Jun 15 2004