A115376 <h[d+1,d-1],s[d,d]*s[d,d]*s[d,d]> 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

2,3

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).

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

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 *)

Prog

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

Crossrefs

Cf. A115375, A082424, A008763, A082437.

Sequence in context: A026547 A081283 A058567 * A076650 A068408 A186696

Adjacent sequences: A115373 A115374 A115375 * A115377 A115378 A115379

Keyword

nonn,easy

Author

Mike Zabrocki, Jan 21 2006

Status

approved