The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A374722 Number of nonisomorphic spanning trees of the nC_5-snake with constant distance between cutpoints. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the number of spanning trees of the cyclic snake formed with n copies of the cycle on 5 vertices. A cyclic snake is a connected graph whose block-cutpoint is a path and all its n blocks are isomorphic to the cycle C_m. REFERENCES Christian Barrientos, Graceful labelings of cyclic snakes, Ars Combin., 60 (2001), 85-96. LINKS Table of n, a(n) for n=1..25. Index entries for linear recurrences with constant coefficients, signature (5,5,-25). 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) EXAMPLE For n=2, a(2)=6 because there are 6 spanning trees of 2C_5-snake __ __ __ __ __ __ __ __, __ __ __ __|__ __ __, __ __ __ \/__ __ __, __ __ __ __ __ __ __|__ __, __ __ __|__ __, __ __|__ __ | |__ 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 *) PROG (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 CROSSREFS Cf. A374721. Sequence in context: A293121 A026982 A051197 * A334328 A324064 A050212 Adjacent sequences: A374719 A374720 A374721 * A374723 A374724 A374725 KEYWORD nonn,easy,changed AUTHOR Christian Barrientos, Jul 17 2024 EXTENSIONS a(25) corrected by Georg Fischer, Aug 09 2024 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 12 15:28 EDT 2024. Contains 375853 sequences. (Running on oeis4.)