OFFSET
0,1
COMMENTS
The sequence has been extended to n = 0 using the linear recurrence. This is consistent with the number of edge covers on the house graph which is the graph obtained from the first Plummer-Toft graph after removing 1 vertex with its 3 incident edges. - Andrew Howroyd, Dec 09 2024
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..500
Eric Weisstein's World of Mathematics, Edge Cover.
Eric Weisstein's World of Mathematics, Plummer-Toft Graph.
Index entries for linear recurrences with constant coefficients, signature (11,-24,-21,33,34,8).
FORMULA
G.f.: (26 - 23*x - 82*x^2 + 105*x^3 + 178*x^4 + 56*x^5)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)). - Andrew Howroyd, Dec 09 2024
a(n) = 11*a(n-1)-24*a(n-2)-21*a(n-3)+33*a(n-4)+34*a(n-5)+8*a(n-6). - Eric W. Weisstein, Sep 05 2025
MATHEMATICA
LinearRecurrence[{11, -24, -21, 33, 34, 8}, {263, 2187, 17304, 133369, 1015455, 7687086}, {0, 20}]
CoefficientList[Series[-((263 - 706 x - 441 x^2 + 1036 x^3 + 940 x^4 + 208 x^5)/((-1 + x + x^2) (-1 + 3 x + 2 x^2) (-1 + 7 x + 4 x^2))), {x, 0, 20}], x]
PROG
(PARI) Vec( (26 - 23*x - 82*x^2 + 105*x^3 + 178*x^4 + 56*x^5)/((1 - x - x^2)*(1 - 3*x - 2*x^2)*(1 - 7*x - 4*x^2)) + O(x^25) ) \\ Andrew Howroyd, Dec 09 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 09 2024
EXTENSIONS
a(0)=26 prepended and terms a(9) onwards by Andrew Howroyd, Dec 09 2024
STATUS
approved