A300848 Number of 5-cycles in the n-Keller graph.

0, 192, 3932352, 14196341760, 27956664625152, 42824416956923904, 57511921349407752192, 71286632288209906434048, 83776042661497348461428736, 94866764955475116656494116864, 104613452872280139876815553429504, 113161952423983070455749407812878336

Offset

1,2

Comments

Terms satisfy an order-42 linear recurrence (with large coefficients). - Eric W. Weisstein, Mar 20 2018

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Keller Graph

Index entries for linear recurrences with constant coefficients, order 42.

Formula

a(n) = 2^(-1 + 2*n)*((1323*(5*3^(1 + 2*n) + 5*3^(1 + 3*n) - 5*3^(1 + n)*4^n + 5*3^n*4^(1 + 2*n) - 5*6^(1 + 2*n) - 5*7^n + 5*2^(1 + 4*n)*9^n + 5*16^n - 5*21^n - 5*2^(1 + 2*n)*27^n + 5*28^n - 61^n - 5*64^n + 5*81^n - 5*192^n + 256^n) + 5*n*(-9*7^n*(225 + 140*3^n + 216*n) + 49*(4*27^(1 + n) + 3^(3 + 2*n)*(7 - 3*2^(1 + 2*n) + 6*n) + 27*(-1 - 64^n - 3*n + 3*n^2 + n^3 + 2^(1 + 4*n)*(2 + n) - 2^(1 + 2*n)*n*(3 + n)) + 3^n*(67 + 27*4^(1 + 2*n) + 129*n + 92*n^2 - 27*2^(1 + 2*n)*(5 + 3*n)))))/6615). - Eric W. Weisstein, Mar 20 2018

Prog

(PARI) \\ needs G function from A300818
seq(n)={my(q2=G(n, 2, [0..3]), q3=G(n, 3, [0..15]), q5=G(n, 5, [0..255]));
vector(n, n, (q5[n] + 3*q3[n]*(1-4*q2[n]/4^n)))} \\ Andrew Howroyd, Mar 14 2018

Crossrefs

Cf. A300818 (3-cycles), A300842 (4-cycles), A300849 (6-cycles).

Sequence in context: A008698 A282541 A202930 * A340352 A012856 A114859

Adjacent sequences: A300845 A300846 A300847 * A300849 A300850 A300851

Keyword

nonn

Author

Eric W. Weisstein, Mar 13 2018

Extensions

Terms a(7) and beyond from Andrew Howroyd, Mar 14 2018

Status

approved