A115375
where h[d,d] is a homogeneous symmetric function, s[d,d] is a Schur function indexed by two parts, * represents the Kronecker product and <, > is the standard scalar product on symmetric functions.
1, 1, 4, 5, 12, 15, 30, 37, 65, 80, 128, 156, 234, 282, 402, 480, 657, 777, 1030, 1207, 1558, 1811, 2286, 2637, 3267, 3742, 4562, 5192, 6242, 7062, 8388, 9438, 11091, 12417, 14454, 16107, 18592, 20629, 23632, 26117, 29715, 32718, 36996, 40594
Offset: 0
References
- M. W. Hero and J. F. Willenbring, Stable Hilbert series as related to the measurement of quantum entanglement, Discrete Math., 309 (2010), 6508-6514.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-7,2,8,2,-7,-3,4,1,-1).
Programs
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PARI
Vec((1 - x^2 + x^4) / ((1 - x)^6*(1 + x)^4*(1 + x + x^2)) + O(x^40)) \\ Colin Barker, May 10 2019
Formula
G.f.: (1 - x^2 + x^4) / ((1 - x)^6*(1 + x)^4*(1 + x + x^2)).
a(n) = a(n-1) + 4*a(n-2) - 3*a(n-3) - 7*a(n-4) + 2*a(n-5) + 8*a(n-6) + 2*a(n-7) - 7*a(n-8) - 3*a(n-9) + 4*a(n-10) + a(n-11) - a(n-12) for n>11. - Colin Barker, May 10 2019