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A301774 Number of chordless cycles in the (2n+1)-prism graph. 1
2, 12, 30, 74, 200, 522, 1362, 3572, 9350, 24474, 64080, 167762, 439202, 1149852, 3010350, 7881194, 20633240, 54018522, 141422322, 370248452, 969323030, 2537720634, 6643838880, 17393796002, 45537549122, 119218851372, 312119004990, 817138163594, 2139295485800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence extended to a(1) using the formula/recurrence (actual count for the 3-prism is 0, which reproduces A301775).

LINKS

Table of n, a(n) for n=1..29.

Eric Weisstein's World of Mathematics, Chordless Cycle

Eric Weisstein's World of Mathematics, Prism Graph

Index entries for linear recurrences with constant coefficients, signature (2, 1, 2, -1).

FORMULA

a(n) = lucasl(2*n + 1) + 2*cos((2*n + 1)*Pi/3).

a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4).

G.f.: -2*(-1 - 4*x - 2*x^2 + x^3)/(1 - 2*x - x^2 - 2*x^3 + x^4).

MATHEMATICA

Table[LucasL[2 n + 1] + 2 Cos[(2 n + 1) Pi/3], {n, 20}]

LinearRecurrence[{2, 1, 2, -1}, {2, 12, 30, 74}, 20]

CoefficientList[Series[-2 (-1 - 4 x - 2 x^2 + x^3)/(1 - 2 x - x^2 - 2 x^3 + x^4), {x, 0, 20}], x]

CROSSREFS

Cf. A301775.

Sequence in context: A127118 A259127 A296257 * A286230 A083175 A019258

Adjacent sequences:  A301771 A301772 A301773 * A301775 A301776 A301777

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Mar 26 2018

STATUS

approved

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Last modified August 19 08:17 EDT 2019. Contains 326115 sequences. (Running on oeis4.)