OFFSET
0,1
COMMENTS
Number of connected induced subgraphs in the n-dipyramidal graph (for n >=3).
LINKS
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph
Index entries for linear recurrences with constant coefficients, signature (5, -9, 7, -2).
FORMULA
a(n) = 3*2^n + n^2 - n.
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
G.f.: (3 - 9*x + 11*x^2 - 7*x^3)/((-1 + x)^3*(-1 + 2*x)).
MATHEMATICA
Table[3 2^n + n^2 - n, {n, 0, 40}]
LinearRecurrence[{5, -9, 7, -2}, {6, 14, 30, 60}, {0, 20}]
CoefficientList[Series[(3 - 9 x + 11 x^2 - 7 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 08 2019
STATUS
approved