login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

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