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A297661 a(n) = n + 2*cos((n*Pi)/3) + Lucas(n). 0
3, 4, 5, 10, 17, 26, 37, 54, 83, 132, 211, 336, 535, 856, 1377, 2222, 3589, 5798, 9369, 15146, 24495, 39624, 64103, 103708, 167787, 271468, 439229, 710674, 1149881, 1860530, 3010381, 4870878, 7881227, 12752076, 20633275, 33385320, 54018559, 87403840, 141422361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also the number of chordless cycles in the n-prism graph for n >= 4.

LINKS

Table of n, a(n) for n=1..39.

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 (4, -6, 4, 0, -2, 1).

FORMULA

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - 2*a(n-5) + a(n-6).

G.f.: x*(-3 + 8*x - 7*x^2 - 2*x^3 + 9*x^4 - 4*x^5)/((-1 + x)^2*(-1 + 2*x - x^2 + x^4)).

MATHEMATICA

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

LinearRecurrence[{4, -6, 4, 0, -2, 1}, {3, 4, 5, 10, 17, 26}, 20]

CoefficientList[Series[(-3 + 8 x - 7 x^2 - 2 x^3 + 9 x^4 - 4 x^5)/((-1 + x)^2 (-1 + 2 x - x^2 + x^4)), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A082612 A170926 A122413 * A136366 A123820 A261903

Adjacent sequences:  A297658 A297659 A297660 * A297662 A297663 A297664

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Jan 02 2018

STATUS

approved

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Last modified February 24 17:29 EST 2020. Contains 332209 sequences. (Running on oeis4.)