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A290764 Number of (non-null) connected induced subgraphs in the 2 X n king graph. 0
3, 15, 54, 174, 537, 1629, 4908, 14748, 44271, 132843, 398562, 1195722, 3587205, 10761657, 32285016, 96855096, 290565339, 871696071, 2615088270, 7845264870, 23535794673, 70607384085, 211822152324, 635466457044, 1906399371207, 5719198113699, 17157594341178 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..27.

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, King Graph

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

Index entries for linear recurrences with constant coefficients, signature (5, -7, 3).

FORMULA

a(n) = 3/4*(3^(n + 1) - 2*n - 3).

a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).

G.f.: -((3 x)/((-1 + x)^2 (-1 + 3 x))).

MATHEMATICA

Table[3/4 (3^(n + 1) - 2 n - 3), {n, 20}]

LinearRecurrence[{5, -7, 3}, {3, 15, 54}, 40]

CoefficientList[Series[-(3/((-1 + x)^2 (-1 + 3 x))), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A212869 A298178 A147618 * A286986 A261565 A085480

Adjacent sequences:  A290761 A290762 A290763 * A290765 A290766 A290767

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 10 2017

STATUS

approved

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Last modified January 27 02:46 EST 2020. Contains 331291 sequences. (Running on oeis4.)