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 144.
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
G.f.: (1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 66*x^5 + 40*x^6 - 15*x^7 + 3*x^8) / (1 - x)^9.
From Colin Barker, Nov 11 2017: (Start)
a(n) = (40320 - 22704*n + 33868*n^2 - 16996*n^3 + 6405*n^4 - 616*n^5 + 42*n^6 - 4*n^7 + 5*n^8) / 40320.
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.
(End)
MAPLE
-(3*x^8-15*x^7+40*x^6-66*x^5+81*x^4-60*x^3+29*x^2-8*x+1)/(x-1)^9 ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;
MATHEMATICA
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 1, 2, 6, 21, 75, 253, 774, 2130}, 40] (* Harvey P. Dale, Dec 24 2023 *)
PROG
(PARI) Vec((1 - 8*x + 29*x^2 - 60*x^3 + 81*x^4 - 66*x^5 + 40*x^6 - 15*x^7 + 3*x^8) / (1 - x)^9 + O(x^40)) \\ Colin Barker, Nov 11 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 08 2017
STATUS
approved