|
%I #8 May 10 2019 06:51:21
%S 1,1,4,5,12,15,30,37,65,80,128,156,234,282,402,480,657,777,1030,1207,
%T 1558,1811,2286,2637,3267,3742,4562,5192,6242,7062,8388,9438,11091,
%U 12417,14454,16107,18592,20629,23632,26117,29715,32718,36996,40594
%N <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.
%D M. W. Hero and J. F. Willenbring, Stable Hilbert series as related to the measurement of quantum entanglement, Discrete Math., 309 (2010), 6508-6514.
%H Colin Barker, <a href="/A115375/b115375.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-7,2,8,2,-7,-3,4,1,-1).
%F G.f.: (1 - x^2 + x^4) / ((1 - x)^6*(1 + x)^4*(1 + x + x^2)).
%F 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
%o (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
%Y Cf. A115376, A082424, A008763, A082437.
%K nonn,easy
%O 0,3
%A _Mike Zabrocki_, Jan 21 2006
|
