A295168 Chromatic invariant of the 2n-crossed prism graph.

1, 11, 85, 521, 2869, 15017, 76717, 387425, 1945957, 9749753, 48793309, 244064849, 1220539285, 6103163369, 30516824461, 152586284993, 762936045253, 3814690056665, 19073471123773, 95367399659057, 476837091094261, 2384185650506441, 11920928661476845

Offset

1,2

Comments

Extended to a(1) using formula/recurrence.

Links

Table of n, a(n) for n=1..23.

Eric Weisstein's World of Mathematics, Chromatic Invariant

Eric Weisstein's World of Mathematics, Crossed Prism Graph

Index entries for linear recurrences with constant coefficients, signature (9, -24, 20).

Formula

a(n) = 5^n - 2^(n - 1)*(3*n + 1).

a(n) = 9*a(n-1) - 24*a(n-2) + 20*a(n-3).

G.f. = x*(-1 - 2*x - 10*x^2)/((-1 + 2*x)^2 (-1 + 5*x)).

Mathematica

Table[5^n - 2^(n - 1) (3 n + 1), {n, 20}]
LinearRecurrence[{9, -24, 20}, {1, 11, 85}, 20]
CoefficientList[Series[(-1 - 2 x - 10 x^2)/((-1 + 2 x)^2 (-1 + 5 x)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A026783 A244975 A271558 * A001240 A129180 A082365

Adjacent sequences: A295165 A295166 A295167 * A295169 A295170 A295171

Keyword

nonn,easy

Author

Eric W. Weisstein, Nov 16 2017

Status

approved