A374722 Number of nonisomorphic spanning trees of the nC_5-snake with constant distance between cutpoints.
1, 6, 24, 120, 570, 2850, 14100, 70500, 351750, 1758750, 8790000, 43950000, 219731250, 1098656250, 5493187500, 27465937500, 137329218750, 686646093750, 3433228125000, 17166140625000, 85830691406250, 429153457031250, 2145767226562500, 10728836132812500, 53644180371093750
Offset: 1
Examples
For n=2, a(2)=6 because there are 6 spanning trees of 2C_5-snake
__ __ __ __ __ __ __ __, __ __ __ __|__ __ __, __ __ __ \/__ __ __,
__ __ __
__ __ __ __|__ __, __ __ __|__ __, __ __|__ __
| |__
References
- Christian Barrientos, Graceful labelings of cyclic snakes, Ars Combin., 60 (2001), 85-96.
Links
- Index entries for linear recurrences with constant coefficients, signature (5,5,-25).
Crossrefs
Cf. A374721.
Programs
-
Mathematica
Drop[CoefficientList[Series[x*(1 + x - 11*x^2 - 5*x^3)/((1 - 5*x)*(1 - 5*x^2)),{x,0,30}],x],1] (* Georg Fischer, Aug 09 2024 *) -
PARI
for(n=1, 30, print1(if(n==1,1,(3/2)*(3* 5^(n - 2) + 5^floor((n - 2)/2))),",")) \\ Georg Fischer, Aug 09 2024
Formula
a(n) = (3/2)*(3* 5^(n - 2) + 5^floor((n - 2)/2)) for n > 1.
From Stefano Spezia, Jul 23 2024: (Start)
G.f.: x*(1 + x - 11*x^2 - 5*x^3)/((1 - 5*x)*(1 - 5*x^2)).
E.g.f.: (24 + 10*x - 9*cosh(5*x) - 15*cosh(sqrt(5)*x) - 9*sinh(5*x) - 3*sqrt(5)*sinh(sqrt(5)*x))/50. (End)
Extensions
a(25) corrected by Georg Fischer, Aug 09 2024
Comments