A307621 Number of cycles in the n-dipyramidal graph.

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

Table of n, a(n) for n=1..40.

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

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

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

Adjacent sequences: A307618 A307619 A307620 * A307622 A307623 A307624

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 19 2019

Status

approved