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 17.
Index entries for linear recurrences with constant coefficients, signature (8,-26,45,-45,26,-8,1).
FORMULA
From Colin Barker, Nov 10 2017: (Start)
G.f.: (1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 13*x^5 + x^7) / ((1 - x)^5*(1 - 3*x + x^2)).
a(n) = (1/60)*(3*2^(1-n)*(5*2^(n+1) - (3-sqrt(5))^n*(-5+sqrt(5)) + (3+sqrt(5))^n*(5+sqrt(5))) - 190*n + 115*n^2 - 50*n^3 + 5*n^4) for n > 0.
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 > 7.
(End)
MAPLE
cn := [1, -7, 20, -29, 25, -13, 0, 1] ;
p := add(cn[i]*x^(i-1), i=1..nops(cn)) ;
q := (1-x)^5*(1-3*x+x^2) ;
taylor(p/q, x=0, 40) ;
gfun[seriestolist](%) ;
PROG
(PARI) Vec((1 - 7*x + 20*x^2 - 29*x^3 + 25*x^4 - 13*x^5 + x^7) / ((1 - x)^5*(1 - 3*x + x^2)) + O(x^40)) \\ Colin Barker, Nov 10 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Nov 07 2017
STATUS
approved