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A290720 a(n) = 2*3^n + 4^n + 3*n. 1
3, 13, 40, 127, 430, 1525, 5572, 20779, 78682, 301537, 1166704, 4548631, 17840134, 70297549, 278001436, 1102439683, 4381060786, 17438149561, 69494317768, 277202429935, 1106485196638, 4418967217573, 17654948163700, 70557030535387, 282039835783690, 1127594484061585 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For n >= 1, also the number of (non-null) connected induced subgraphs in the n-book graph.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1659

Eric Weisstein's World of Mathematics, Book Graph

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Index entries for linear recurrences with constant coefficients, signature (9, -27, 31, -12).

FORMULA

a(n) = 2*3^n + 4^n + 3*n.

a(n) = 9*a(n-1) - 27*a(n-2) + 31*a(n-3) - 12*a(n-4).

G.f.: (3 - 14 x + 4 x^2 + 25 x^3)/((-1 + x)^2 (1 - 7 x + 12 x^2)).

MAPLE

seq(2*3^n + 4^n + 3*n, n=0..30); # Robert Israel, Aug 09 2017

MATHEMATICA

Table[2 3^n + 4^n + 3 n, {n, 0, 20}]

LinearRecurrence[{9, -27, 31, -12}, {13, 40, 127, 430}, {0, 20}]

CoefficientList[Series[(3 - 14 x + 4 x^2 + 25 x^3)/((-1 + x)^2 (1 - 7 x + 12 x^2)), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A018492 A227446 A059020 * A289654 A095109 A259764

Adjacent sequences:  A290717 A290718 A290719 * A290721 A290722 A290723

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 09 2017

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)