

A290775


Number of 5cycles in the ntriangular 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
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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(n1)  21*a(n2) + 35*a(n3)  35*a(n4) + 21*a(n5)  7*a(n6) + a(n7).
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 (3cycles in the triangular honeycomb bishop graph), A051843 (4cycles), A290779 (6cycles).
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



