A115376 where h[d+1,d-1] 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, 5, 6, 16, 20, 41, 51, 90, 111, 177, 216, 321, 387, 546, 651, 882, 1041, 1366, 1597, 2042, 2367, 2962, 3407, 4187, 4782, 5787, 6567, 7842, 8847, 10443, 11718, 13692, 15288, 17703, 19677, 22603, 25018, 28532, 31458, 35644, 39158, 44108, 48294

Offset: 2

Author

Mike Zabrocki, Jan 21 2006

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (1,4,-3,-7,2,8,2,-7,-3,4,1,-1).

Crossrefs

Cf. A115375, A082424, A008763, A082437.

Programs

Mathematica

Drop[CoefficientList[Series[x^2/((1-x)(1-x^2)^4(1-x^3)),{x,0,50}],x],2]  (* Harvey P. Dale, Aug 24 2011 *)

PARI

Vec(x^2 / ((1 - x)^6*(1 + x)^4*(1 + x + x^2)) + O(x^50)) \\ Colin Barker, May 10 2019

Formula

G.f.: x^2 / ((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