A215774 Number of undirected labeled graphs on n+4 nodes with exactly n cycle graphs as connected components.

0, 12, 127, 742, 3157, 10857, 31899, 82929, 195459, 425139, 864864, 1662661, 3045406, 5349526, 9059946, 14858646, 23684298, 36804558, 55902693, 83180328, 121478203, 174416935, 246559885, 343600335, 472575285, 642108285, 862683822, 1146955887, 1510093452

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: (43*x^3+31*x^2+19*x+12)*x/(1-x)^9.

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(15*n^3+30*n^2+245*n+286)/5760.

Example

a(1) = 12 = 4!/2: (1-2-3-4-5-1), (1-2-3-5-4-1), (1-2-4-3-5-1), (1-2-4-5-3-1), (1-2-5-3-4-1), (1-2-5-4-3-1), (1-3-2-4-5-1), (1-3-2-5-4-1), (1-3-4-2-5-1), (1-3-5-2-4-1), (1-4-2-3-5-1), (1-4-3-2-5-1).

Maple

a:= n-> (6864+(20180+(22980+(13295+(4536+(1070+(180+15*n)*
               n)*n)*n)*n)*n)*n)*n/5760:
seq(a(n), n=0..40);

Prog

(PARI) a(n)=n*(n+1)*(n+2)*(n+3)*(n+4)*(15*n^3+30*n^2+245*n+286)/5760 \\ Charles R Greathouse IV, May 30 2026

Crossrefs

A diagonal of A215771.

Sequence in context: A124797 A204768 A045508 * A275941 A173359 A199037

Adjacent sequences: A215771 A215772 A215773 * A215775 A215776 A215777

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 23 2012

Status

approved