A297619 a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3), a(1) = 0, a(2) = 0, a(3) = 8.

0, 0, 8, 16, 48, 96, 224, 448, 960, 1920, 3968, 7936, 16128, 32256, 65024, 130048, 261120, 522240, 1046528, 2093056, 4190208, 8380416, 16769024, 33538048, 67092480, 134184960, 268402688, 536805376, 1073676288, 2147352576, 4294836224, 8589672448, 17179607040

Offset

1,3

Comments

Number of minimum distinguishing (2-)labelings of the n-pan graph for n >= 3.

Links

Muniru A Asiru, Table of n, a(n) for n = 1..500

J. Tymoczko, Distinguishing numbers for graphs and groups, arXiv:math/0406542 [math.CO], 2004-2005.

Eric Weisstein's World of Mathematics, Pan Graph

Index entries for linear recurrences with constant coefficients, signature (2, 2, -4).

Formula

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

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

G.f.: 8*x^3/(1 - 2*x - 2*x^2 + 4*x^3).

Maple

f := proc(n) option remember:
if n = 1 then 0 elif n = 2 then 0 elif n = 3 then 8 elif  n >= 4 then 2 * procname(n-1) + 2* procname(n-2) - 4 * procname(n-3) fi; end:
A297619:=[seq(f(n), n = 0..10^2)]; # Muniru A Asiru, Jan 28 2018

Mathematica

Table[2^(n + 1) - 2^(Floor[n/2] + 2), {n, 20}]
LinearRecurrence[{2, 2, -4}, {0, 0, 8}, 20]
CoefficientList[Series[(8 x^2)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 20}], x]

Prog

(PARI) first(n) = Vec(8*x^3/(1 - 2*x - 2*x^2 + 4*x^3) + O(x^(n+1)), -n) \\ Iain Fox, Jan 02 2018
(GAP) a := [0, 0, 8];; for n in [4..500] do a[n] := 2 * a[n-1] + 2 * a[n-2] - 4 * a[n-3]; od; a; # Muniru A Asiru, Jan 28 2018

Crossrefs

Sequence in context: A266159 A022444 A089828 * A188825 A214204 A335771

Adjacent sequences: A297616 A297617 A297618 * A297620 A297621 A297622

Keyword

nonn,easy

Author

Eric W. Weisstein, Jan 01 2018

Status

approved