OFFSET
1,1
REFERENCES
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..750
F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.
F. Faase, Results from the counting program
Index entries for linear recurrences with constant coefficients, signature (16,136,-460,432,256).
FORMULA
a(1) = 6,
a(2) = 204,
a(3) = 4152,
a(4) = 90012,
a(5) = 1916640,
a(6) = 41086080, and
a(n) = 16a(n-1) + 136a(n-2) - 460a(n-3) + 432a(n-4) + 256a(n-5).
G.f.: 6*x*(256*x^5 -504*x^4 +234*x^3 -12*x^2 -18*x -1)/(256*x^5 +432*x^4 -460*x^3 +136*x^2 +16*x -1). - Colin Barker, Aug 30 2012
MATHEMATICA
CoefficientList[Series[6 (256 x^5 - 504 x^4 + 234 x^3 - 12 x^2 - 18 x - 1)/(256 x^5 + 432 x^4 - 460 x^3 + 136 x^2 + 16 x - 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 14 2013 *)
LinearRecurrence[{16, 136, -460, 432, 256}, {6, 204, 4152, 90012, 1916640, 41086080}, 20] (* Harvey P. Dale, May 17 2024 *)
PROG
(Magma) I:=[6, 204, 4152, 90012, 1916640, 41086080]; [n le 6 select I[n] else 16*Self(n-1)+136*Self(n-2)-460*Self(n-3)+432*Self(n-4)+256*Self(n-5): n in [1..20]]; // Vincenzo Librandi, Oct 14 2013
(PARI) Vec(6*x*(256*x^5-504*x^4+234*x^3-12*x^2-18*x-1)/(256*x^5+432*x^4-460*x^3+136*x^2+16*x-1)+O(x^99)) \\ Charles R Greathouse IV, Jun 23 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009
STATUS
approved