OFFSET
0,3
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO] (2017), Table 2 No 28.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
From Colin Barker, Nov 10 2017: (Start)
G.f.: (1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 70*x^5 + 40*x^6 - 10*x^7 + 2*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>8.
a(n) = (40320 - 14640*n + 15724*n^2 - 3780*n^3 + 3885*n^4 - 1680*n^5 + 546*n^6 - 60*n^7 + 5*n^8) / 40320.
(End)
MAPLE
cn := [1, -8, 29, -60, 81, -70, 40, -10, 2] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^9 ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;
PROG
(PARI) Vec((1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 70*x^5 + 40*x^6 - 10*x^7 + 2*x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Nov 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 07 2017
STATUS
approved