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 1 No 80.
Index entries for linear recurrences with constant coefficients, signature (8,-26,45,-45,26,-8,1).
FORMULA
G.f.: (1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 10*x^5 + 2*x^6) / ((1 - x)^5*(1 - 3*x + x^2)).
From Colin Barker, Nov 09 2017: (Start)
a(n) = (1/60)*(-3*2^(2-n)*(15*2^n + 2*(-5+sqrt(5))*(3+sqrt(5))^n - 2*(3-sqrt(5))^n*(5+sqrt(5))) + 80*n - 85*n^2 + 10*n^3 - 5*n^4).
a(n) = 8*a(n-1) - 26*a(n-2) + 45*a(n-3) - 45*a(n-4) + 26*a(n-5) - 8*a(n-6) + a(n-7) for n>6.
(End)
MAPLE
(1 -7*x +20*x^2 -29*x^3 +25*x^4 -10*x^5 +2*x^6)/((1 -x)^5*(1 -3*x +x^2)) ;
taylor(%, x=0, 40) ;
gfun[seriestolist](%) ;
PROG
(PARI) Vec((1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 10*x^5 + 2*x^6) / ((1 - x)^5*(1 - 3*x + x^2)) + O(x^30)) \\ Colin Barker, Nov 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 09 2017
STATUS
approved