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

1,2

Comments

Extended to n=1 and 2 using the closed-form sum. - Eric W. Weisstein, May 04 2017

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

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

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 *)

Prog

(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

Crossrefs

Cf. A002807, A192856.

Sequence in context: A256752 A018963 A217886 * A030815 A030880 A030926

Adjacent sequences: A234624 A234625 A234626 * A234628 A234629 A234630

Keyword

nonn

Author

Eric W. Weisstein, Dec 28 2013

Extensions

a(12)-a(14) from Eric W. Weisstein, Apr 09 2014

a(15)-a(20) from Andrew Howroyd, Mar 05 2016

Status

approved