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A290775 Number of 5-cycles in the n-triangular honeycomb bishop graph. 3
0, 0, 2, 24, 138, 532, 1596, 4032, 8988, 18216, 34254, 60632, 102102, 164892, 256984, 388416, 571608, 821712, 1156986, 1599192, 2174018, 2911524, 3846612, 5019520, 6476340, 8269560, 10458630, 13110552, 16300494, 20112428, 24639792, 29986176, 36266032, 43605408, 52142706 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Graph Cycle

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = 2/5 * binomial(n + 1, 4)*(8 - 7*n + 2*n^2).

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

G.f.: -((2 x (x^2 + 5 x^3 + 6 x^4))/(-1 + x)^7).

MATHEMATICA

Table[2/5 Binomial[n + 1, 4] (8 - 7 n + 2 n^2), {n, 20}]

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 2, 24, 138, 532, 1596}, 20]

CoefficientList[Series[-((2 (x^2 + 5 x^3 + 6 x^4))/(-1 + x)^7), {x, 0, 20}], x]

PROG

(PARI) a(n)=n*(2*n^5 - 11*n^4 + 20*n^3 - 5*n^2 - 22*n + 16)/60 \\ Charles R Greathouse IV, Aug 10 2017

CROSSREFS

Cf. A034827 (3-cycles in the triangular honeycomb bishop graph), A051843 (4-cycles), A290779 (6-cycles).

Sequence in context: A098455 A261475 A078994 * A000185 A264566 A163752

Adjacent sequences:  A290772 A290773 A290774 * A290776 A290777 A290778

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 10 2017

STATUS

approved

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Last modified February 21 14:29 EST 2018. Contains 299414 sequences. (Running on oeis4.)