A290775 Number of 5-cycles in the n-triangular honeycomb bishop graph.

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

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