A347503 Number of dominating sets in the n-dipyramidal graph.

5, 13, 29, 57, 115, 229, 453, 897, 1775, 3513, 6957, 13785, 27331, 54221, 107629, 213761, 424767, 844465, 1679605, 3342057, 6652563, 13247093, 26387445, 52578561, 104796015, 208927849, 416634077, 831021241, 1657909763, 3308218269, 6602455645, 13179196417

Offset

1,1

Comments

Sequence extended to a(1) using the formula/recurrence.

Links

Table of n, a(n) for n=1..32.

Eric Weisstein's World of Mathematics, Dipyramidal Graph

Eric Weisstein's World of Mathematics, Dominating Set

Index entries for linear recurrences with constant coefficients, signature (4,-4,0,-1,2).

Formula

a(n)=4*a(n-1)-4*a(n-2)-a(n-4)+2*a(n-5).

G.f.: -x*(5-7*x-3*x^2-7*x^3+8*x^4)/((-1+x)*(-1+2*x)*(-1+x+x^2+x^3)).

Mathematica

Table[RootSum[-1 - # - #^2 + #^3 &, #^n &] + 3 2^n - 2, {n, 20}]
CoefficientList[Series[-(5 - 7 x - 3 x^2 - 7 x^3 + 8 x^4)/((-1 + x) (-1 + 2 x) (-1 + x + x^2 + x^3)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A273026 A273077 A160430 * A023617 A023619 A020576

Adjacent sequences: A347500 A347501 A347502 * A347504 A347505 A347506

Keyword

nonn

Author

Eric W. Weisstein, Sep 04 2021

Status

approved