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A347503
Number of dominating sets in the n-dipyramidal graph.
0
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
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Dominating Set
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
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 04 2021
STATUS
approved