A335768 a(n) is the number of odd-balanced unimodal sequences of weight 2n+2.
1, 2, 5, 9, 16, 29, 48, 77, 123, 191, 290, 436, 643, 936, 1352, 1927, 2720, 3810, 5287, 7282, 9965, 13539, 18280, 24545, 32769, 43519, 57522, 75667, 99092, 129237, 167862, 217192, 280003, 359695, 460513, 587702
Offset: 0
Keywords
Examples
a(4) = 16, the relevant odd-balanced unimodal sequences being [10], [1,8,1], [8,2], [2,8], [1,1,6,1,1], [2,6,2], [4,6], [6,4], [1,6,2,1], [1,2,6,1], [1,1,1,4,1,1,1], [1,2,4,2,1], [1,1,2,4,1,1], [1,1,4,2,1,1], [3,4,3], [1,1,1,1,2,1,1,1,1].
Links
- B. Kim, S. Lim, and J. Lovejoy, Odd-balanced unimodal sequences and related functions: parity, mock modularity and quantum modularity, Proceedings of the American Mathematical Society, 144 (2016), 3687-3700.
Programs
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PARI
my(N=44, q='q+O('q^N)); Vec( 1/(1-q) + sum(n=1, N, q^n * prod(k=1,n, (1+q^k)^2) / prod(k=1,n+1, 1-q^(2*k-1)) ) ) \\ Joerg Arndt, Jun 22 2020
Formula
G.f.: 1/(1-q) + Sum_{n>=1} q^n*(Product_{k=1..n} (1+q^k)^2)/(Product_{k=1..n+1} (1-q^(2*k-1))).
Comments