A115375 <h[d,d],s[d,d]*s[d,d]*s[d,d]> 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

0,3

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).

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

Prog

(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

Crossrefs

Cf. A115376, A082424, A008763, A082437.

Sequence in context: A130011 A050022 A137619 * A212114 A269227 A103650

Adjacent sequences: A115372 A115373 A115374 * A115376 A115377 A115378

Keyword

nonn,easy

Author

Mike Zabrocki, Jan 21 2006

Status

approved