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A295168 Chromatic invariant of the 2n-crossed prism graph. 0

%I #4 Nov 16 2017 08:11:53

%S 1,11,85,521,2869,15017,76717,387425,1945957,9749753,48793309,

%T 244064849,1220539285,6103163369,30516824461,152586284993,

%U 762936045253,3814690056665,19073471123773,95367399659057,476837091094261,2384185650506441,11920928661476845

%N Chromatic invariant of the 2n-crossed prism graph.

%C Extended to a(1) using formula/recurrence.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ChromaticInvariant.html">Chromatic Invariant</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CrossedPrismGraph.html">Crossed Prism Graph</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9, -24, 20).

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

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

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

%t Table[5^n - 2^(n - 1) (3 n + 1), {n, 20}]

%t LinearRecurrence[{9, -24, 20}, {1, 11, 85}, 20]

%t CoefficientList[Series[(-1 - 2 x - 10 x^2)/((-1 + 2 x)^2 (-1 + 5 x)), {x, 0, 20}], x]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Nov 16 2017

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