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A366506
a(n) = Lucas(n) + 3.
0
4, 6, 7, 10, 14, 21, 32, 50, 79, 126, 202, 325, 524, 846, 1367, 2210, 3574, 5781, 9352, 15130, 24479, 39606, 64082, 103685, 167764, 271446, 439207, 710650, 1149854, 1860501, 3010352, 4870850, 7881199, 12752046, 20633242, 33385285, 54018524, 87403806, 141422327
OFFSET
1,1
COMMENTS
For n >= 3, number of independent vertex sets in the n-dipyramid graph.
LINKS
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Independent Vertex Set
FORMULA
a(n) = A000032(n) + 3.
a(n) = 2*a(n-1) - a(n-3).
G.f.: x*(4-2*x-5*x^2)/(1-2*x+x^3).
MATHEMATICA
LucasL[Range[20]] + 3
Table[LucasL[n] + 3, {n, 20}]
LinearRecurrence[{2, 0, -1}, {4, 6, 7}, 20]
CoefficientList[Series[(4 - 2 x - 5 x^2)/(1 - 2 x + x^3), {x, 0, 20}], x]
CROSSREFS
Cf. A000032 (Lucas numbers).
Sequence in context: A023635 A317649 A265036 * A310652 A310653 A310654
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Oct 11 2023
STATUS
approved