A234627 Numbers of undirected cycles in the n-sun graph.
1, 3, 11, 44, 198, 1036, 6346, 45019, 364039, 3306553, 33328389, 369132782, 4456043300, 58230679722, 818965960156, 12334276322245, 198059886271741, 3377876368962559, 60978094460613103, 1161619710523459392
Offset: 1
Keywords
Links
- Andrew Howroyd and Vaclav Kotesovec, Table of n, a(n) for n = 1..420 (terms 3..50 from Andrew Howroyd; terms 1..2 corrected by _Georg Fischer_, Jan 20 2019)
- Eric Weisstein's World of Mathematics, Graph Cycle
- Eric Weisstein's World of Mathematics, Sun Graph
Programs
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Mathematica
Table[(2 - Binomial[n + 1, 2] + Sum[(k - 1)! (Binomial[n, k] + Sum[n 2^j Binomial[n - j - i - 1, j - 1] Binomial[i + j - 1, i] Binomial[n - 2 j - i, k - j]/j, {j, k}, {i, 0, n - j - k}]), {k, n}])/2, {n, 20}] (* Eric W. Weisstein, Dec 14 2017 *) -
PARI
a(n) = (2 - binomial(n+1, 2) + sum(k=1, n, (k-1)! * (binomial(n, k) + sum(j=1, k, sum(i=0, n-j-k, n*(2^j)*binomial(n-j-i-1, j-1)*binomial(i+j-1, i)*binomial(n-2*j-i, k-j)/j)))))/2; \\ after formula; Michel Marcus, Mar 06 2016
Formula
a(n) = (1/2) * (2 - binomial(n+1, 2) + Sum_{k=1..n} (k-1)! * (binomial(n, k) + Sum_{j=1..k} Sum_{i=0..n-j-k} n*(2^j)*binomial(n-j-i-1, j-1)*binomial(i+j-1, i)*binomial(n-2*j-i, k-j)/j) ). - Andrew Howroyd, Mar 05 2016
a(n) ~ exp(3)/2 * (n-1)!. - Vaclav Kotesovec, Mar 06 2016
Extensions
a(12)-a(14) from Eric W. Weisstein, Apr 09 2014
a(15)-a(20) from Andrew Howroyd, Mar 05 2016
Comments