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A307621
Number of cycles in the n-dipyramidal graph.
0
1, 6, 22, 63, 151, 316, 596, 1037, 1693, 2626, 3906, 5611, 7827, 10648, 14176, 18521, 23801, 30142, 37678, 46551, 56911, 68916, 82732, 98533, 116501, 136826, 159706, 185347, 213963, 245776, 281016, 319921, 362737, 409718, 461126, 517231, 578311, 644652, 716548, 794301
OFFSET
1,2
COMMENTS
Extended to a(1)-a(2) using the formula/recurrence.
For n > 2, also the number of minimal edge cuts in the n-prism graph. - Eric W. Weisstein, Jan 07 2023
LINKS
Eric Weisstein's World of Mathematics, Dipyramidal Graph
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, Minimal Edge Cut
Eric Weisstein's World of Mathematics, Prism Graph
FORMULA
a(n) = n*(n - 1)*(2*n^2 - 4*n + 15)/6 + 1.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
G.f.: x (-1 - x - 2*x^2 - 3*x^3 - x^4)/(-1 + x)^5.
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 6, 22, 63, 151}, 20]
Table[n (n - 1) (2 n^2 - 4 n + 15)/6 + 1, {n, 20}]
CoefficientList[Series[(-1 - x - 2 x^2 - 3 x^3 - x^4)/(-1 + x)^5, {x, 0, 20}], x]
CROSSREFS
Sequence in context: A081282 A001769 A166020 * A257200 A258474 A120477
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Apr 19 2019
STATUS
approved