A300848 - OEIS

%I #18 Mar 17 2024 11:23:19

%S 0,192,3932352,14196341760,27956664625152,42824416956923904,

%T 57511921349407752192,71286632288209906434048,

%U 83776042661497348461428736,94866764955475116656494116864,104613452872280139876815553429504,113161952423983070455749407812878336

%N Number of 5-cycles in the n-Keller graph.

%C Terms satisfy an order-42 linear recurrence (with large coefficients). - _Eric W. Weisstein_, Mar 20 2018

%H Andrew Howroyd, <a href="/A300848/b300848.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphCycle.html">Graph Cycle</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/KellerGraph.html">Keller Graph</a>

%H <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, order 42.

%F 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

%o (PARI) \\ needs G function from A300818

%o seq(n)={my(q2=G(n,2,[0..3]), q3=G(n,3,[0..15]), q5=G(n,5,[0..255]));

%o vector(n,n, (q5[n] + 3*q3[n]*(1-4*q2[n]/4^n)))} \\ _Andrew Howroyd_, Mar 14 2018

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

%K nonn

%O 1,2

%A _Eric W. Weisstein_, Mar 13 2018

%E Terms a(7) and beyond from _Andrew Howroyd_, Mar 14 2018