OFFSET
0,6
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Toufik Mansour, Sherry H. F. Yan and Laura L. M. Yang, Counting occurrences of 231 in an involution, Discrete Mathematics 306 (2006), pages 564-572 (see Corollary 3.5, first case).
Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).
FORMULA
G.f.: x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4.
For n>12, a(n) = 2^(n-17)*(n^3+414*n^2+12227*n-30762)/3.
a(n) = 8*a(n-1)-24*a(n-2)+32*a(n-3)-16*a(n-4) for n>16, n=4, n=11.
MATHEMATICA
CoefficientList[Series[x^5 (1 - x)^2 (4 - 14 x + 8 x^2 + 11 x^3 - 6 x^4 - 2 x^5 + 2 x^6 + 5 x^7 - 2 x^8 + x^9)/(1 - 2 x)^4, {x, 0, 34}], x]
PROG
(PARI) Vec(x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4+O(x^34)) \\ show terms starting with 4.
(Maxima) makelist(coeff(taylor(x^5*(1-x)^2*(4-14*x+8*x^2+11*x^3-6*x^4-2*x^5+2*x^6+5*x^7-2*x^8+x^9)/(1-2*x)^4, x, 0, n), x, n), n, 0, 33);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, May 28 2012
STATUS
approved