A077265 Number of cycles in the n-th order prism graph.

14, 28, 52, 94, 170, 312, 584, 1114, 2158, 4228, 8348, 16566, 32978, 65776, 131344, 262450, 524630, 1048956, 2097572, 4194766, 8389114, 16777768, 33555032, 67109514, 134218430, 268436212, 536871724, 1073742694, 2147484578, 4294968288, 8589935648, 17179870306

Offset: 3

Author

Eric W. Weisstein, Nov 01 2002

Keywords

• nonn
• easy

Comments

Also the number of cycles in the n-th order web graph. - Eric W. Weisstein, Dec 17 2013

Also the number of minimal edge cuts in the n-dipyramidal graph. - Eric W. Weisstein, Oct 30 2024

A subsequence of A290699.

Links

• Eric Weisstein's World of Mathematics, Graph Cycle.
• Eric Weisstein's World of Mathematics, Dipyramidal Graph.
• Eric Weisstein's World of Mathematics, Prism Graph.
• Eric Weisstein's World of Mathematics, Web Graph.
• Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Crossrefs

Cf. A077263, A260699.

Cf. A000079, A002378, A132109.

Programs

Maple

A077265:=n->2^n+n*(n-1); seq(A077265(n), n=3..40); # Wesley Ivan Hurt, May 07 2014

Mathematica

Table[2^n + n*(n - 1), {n, 3, 40}] (* Wesley Ivan Hurt, May 07 2014 *)
LinearRecurrence[{5,-9,7,-2},{14,28,52,94},40] (* Harvey P. Dale, Mar 17 2019 *)

Formula

a(n) = 2^n+n*(n-1). - Eric W. Weisstein, Dec 16 2013

a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4). - Colin Barker, May 06 2014

G.f.: -2*x^3*(6*x^3-19*x^2+21*x-7) / ((x-1)^3*(2*x-1)). - Colin Barker, May 06 2014

a(n) = A000079(n) + A002378(n-1). - Wesley Ivan Hurt, May 07 2014

a(n) = 2*A132109(n-1). - R. J. Mathar, May 23 2016

Extensions

More terms from Eric W. Weisstein, Dec 16 2013