OFFSET
3,2
LINKS
Colin Barker, Table of n, a(n) for n = 3..1000
J. Brunvoll, S. J. Cyvin and B. N. Cyvin, Isomer enumeration of polygonal systems representing polycyclic conjugated hydrocarbons: unbranched catacondensed systems with tetragons and q-gons, J. Molec. Struct. (Theochem), 364 (1996), 1-13, Table 12 with q=9 and alpha=3.
Index entries for linear recurrences with constant coefficients, signature (24,-204,576,1260,-9504,7776,31104,-46656).
FORMULA
G.f.: x^3 + 4*x^4 + 40*x^5 - 6*x^6*(-55 + 851*x - 3708*x^2 - 3273*x^3 + 54540*x^4 - 63828*x^5 - 178848*x^6 + 309096*x^7) / ( (6*x^2-1)^2*(6*x-1)^4 ). - R. J. Mathar, Aug 01 2019
a(n) = 24*a(n-1) - 204*a(n-2) + 576*a(n-3) + 1260*a(n-4) - 9504*a(n-5) + 7776*a(n-6) + 31104*a(n-7) - 46656*a(n-8) for n>13. - Colin Barker, Aug 03 2019
MAPLE
# Exhibit 1
Hra := proc(r::integer, a::integer, q::integer)
binomial(r-1, a-1)*(q-3)+binomial(r-1, a) ;
%*(q-3)^(r-a-1) ;
end proc:
Jra := proc(r::integer, a::integer, q::integer)
binomial(r-2, a-2)*(q-3)^2 +2*binomial(r-2, a-1)*(q-3) +binomial(r-2, a) ;
%*(q-3)^(r-a-2) ;
end proc:
# Exhibit 2
A121126 := proc(r::integer)
q := 9 ;
a := 3 ;
Jra(r, a, q)+binomial(2, r-a)+( 1 +(-1)^(r+a) +(1+(-1)^a)*(1-(-1)^r)*floor((q-3)/2)/2)*Hra(floor(r/2), floor(a/2), q) ;
%/4 ;
end proc:
seq(A121126(n), n=3..30) ; # R. J. Mathar, Aug 01 2019
MATHEMATICA
Join[{1, 4, 40}, LinearRecurrence[{24, -204, 576, 1260, -9504, 7776, 31104, -46656}, {330, 2814, 22464, 174798, 1321920, 9798840, 71383680, 512709912}, 19]] (* Jean-François Alcover, Apr 04 2020 *)
PROG
(PARI) Vec(x^3*(1 - 20*x + 148*x^2 - 390*x^3 - 510*x^4 + 3672*x^5 - 522*x^6 - 9288*x^7 - 5832*x^8 + 15552*x^9 + 11664*x^10) / ((1 - 6*x)^4*(1 - 6*x^2)^2) + O(x^30)) \\ Colin Barker, Aug 03 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 13 2006
STATUS
approved