login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003772 Number of Hamiltonian paths in K_4 X P_n. 1
12, 408, 6648, 90672, 1103088, 12509256, 135409896, 1419480288, 14545113696, 146607233784, 1460033574744, 14411647534224, 141321405768144, 1379055205227432, 13408489143753672, 130019327919243840, 1258252792162873152, 12158637295940721240 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamilton cycles in product graphs

F. Faase, Results from the counting program

Index entries for linear recurrences with constant coefficients, signature (23,-173,421,62,-132,24).

FORMULA

Faase gives a 6-term linear recurrence on his web page:

a(1) = 12,

a(2) = 408,

a(3) = 6648,

a(4) = 90672,

a(5) = 1103088,

a(6) = 12509256,

a(7) = 135409896 and

a(n) = 23a(n-1) - 173a(n-2) + 421a(n-3) + 62a(n-4) - 132a(n-5) + 24a(n-6).

G.f.: 12*x*(24*x^6-164*x^5+398*x^4-275*x^3+55*x^2-11*x-1)/((2*x^2-7*x+1)^2*(6*x^2+9*x-1)). [Colin Barker, Aug 30 2012]

MATHEMATICA

CoefficientList[Series[12(24 x^6 - 164 x^5 + 398 x^4 - 275 x^3 + 55 x^2 - 11 x - 1)/((2 x^2 - 7 x + 1)^2 (6 x^2 + 9 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 14 2013 *)

CROSSREFS

Sequence in context: A202788 A285028 A292784 * A211078 A299382 A197038

Adjacent sequences:  A003769 A003770 A003771 * A003773 A003774 A003775

KEYWORD

nonn,easy

AUTHOR

Frans J. Faase

EXTENSIONS

Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 19 12:38 EST 2018. Contains 317351 sequences. (Running on oeis4.)