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
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).
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