OFFSET
2,2
LINKS
Eric Weisstein's World of Mathematics, Harary Index
Eric Weisstein's World of Mathematics, White Bishop Graph
Index entries for linear recurrences with constant coefficients, signature (2, 2, -6, 0, 6, -2, -2, 1).
FORMULA
a(n) = (21 - 4*n - 42*n^2 + 16*n^3 + 6*n^4 + 3*(-1)^n*(-7 + 4*n + 2*n^2))/96.
a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
G.f.: x^2*(-1 - 3*x - 9*x^2 - x^3 + 2*x^4)/((-1 + x)^5*(1 + x)^3).
MATHEMATICA
Table[(21 - 4 n - 42 n^2 + 16 n^3 + 6 n^4 + 3 (-1)^n (-7 + 4 n + 2 n^2))/96, {n, 20}]
LinearRecurrence[{2, 2, -6, 0, 6, -2, -2, 1}, {1, 5, 21, 47, 104, 182, 318, 490}, 20]
CoefficientList[Series[(-1 - 3 x - 9 x^2 - x^3 + 2 x^4)/((-1 + x)^5 (1 + x)^3), {x, 0, 20}], x]
PROG
(PARI) first(n) = Vec(x^2*(-1 - 3*x - 9*x^2 - x^3 + 2*x^4)/((-1 + x)^5*(1 + x)^3) + O(x^(n+2))) \\ Iain Fox, Dec 07 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Dec 07 2017
STATUS
approved