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

Author

Mike Zabrocki, Jan 21 2006

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A115376, A082424, A008763, A082437.

Programs

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