A287592 Number of connected induced subgraphs on the n-crown graph.

0, 2, 6, 31, 167, 806, 3588, 15233, 62973, 256504, 1036274, 4167659, 16719843, 66985946, 268173264, 1073184709, 4293787577, 17177378732, 68714233758, 274866896783, 1099488558975, 4397998276462, 17592085380956, 70368534462281, 281474540502837, 1125899000872736

Offset

0,2

Comments

Extended to a(0)-a(2) using the closed form.

Links

Table of n, a(n) for n=0..25.

Eric Weisstein's World of Mathematics, Crown Graph

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

Index entries for linear recurrences with constant coefficients, signature (11, -47, 101, -116, 68, -16).

Formula

a(n) = (-1+2^n)^2-(n*(-7+2^(1+n)+n))/2.

a(n) = 11*a(n-1)-47*a(n-2)+101*a(n-3)-116*a(n-4)+68*a(n-5)-16*a(n-6).

G.f.: (x*(2-16*x+59*x^2-94*x^3+52*x^4))/((1-2*x)^2*(-1+x)^3*(-1+4*x)).

Mathematica

Table[(2^n - 1)^2 - 1/2 n (2^(n + 1) + n - 7), {n, 0, 20}]
LinearRecurrence[{11, -47, 101, -116, 68, -16}, {2, 6, 31, 167, 806,
  3588}, {0, 20}]
CoefficientList[Series[(x (2 - 16 x + 59 x^2 - 94 x^3 + 52 x^4))/((1 - 2 x)^2 (-1 + x)^3 (-1 + 4 x)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A231816 A058028 A216834 * A054141 A007710 A275558

Adjacent sequences: A287589 A287590 A287591 * A287593 A287594 A287595

Keyword

nonn,easy

Author

Eric W. Weisstein, May 26 2017

Status

approved