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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A003768 Number of spanning trees with degrees 1 and 3 in W_4 X P_n. 1
2, 16, 144, 1216, 10004, 82608, 682636, 5639688, 46590712, 384898384, 3179752720, 26268806752, 217013752672, 1792809557568, 14810886647616, 122356756509056, 1010822390349184, 8350678243197184, 68987220485229824, 569922160991852032 (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

Bruno Berselli, 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 sequences related to trees

Index entries for linear recurrences with constant coefficients, signature (14,-62,148,-264,336,-256,128,-64).

FORMULA

Faase gives an 8-term linear recurrence on his web page:

a(1) = 2, a(2) = 16, a(3) = 144, a(4) = 1216, a(5) = 10004, a(6) = 82608, a(7) = 682636, a(8) = 5639688, a(9) = 46590712, a(10) = 384898384, a(11) = 3179752720 and

a(n) = 14*a(n-1) - 62*a(n-2) + 148*a(n-3) - 264*a(n-4) + 336*a(n-5) - 256*a(n-6) + 128*a(n-7) - 64*a(n-8).

G.f.: 2*x*(1 -6*x +22*x^2 -52*x^3 +34*x^4 +92*x^5 -222*x^6 +184*x^7 -24*x^8 -64*x^10) / (1 -14*x +62*x^2 -148*x^3 +264*x^4 -336*x^5 +256*x^6 -128*x^7 +64*x^8). [Bruno Berselli, Sep 02 2012]

MATHEMATICA

CoefficientList[Series[2*(1 - 6 x + 22 x^2 - 52 x^3 + 34 x^4 + 92 x^5 - 222 x^6 + 184 x^7 - 24 x^8 - 64 x^10)/(1 - 14 x + 62 x^2 - 148 x^3 + 264 x^4 - 336 x^5 + 256 x^6 - 128 x^7 + 64 x^8), {x, 0, 19}], x] (* Bruno Berselli, Sep 02 2012 *)

PROG

(PARI)

a(n) = if(n<1, 0, if(n<9, [2, 16, 144, 1216, 10004, 82608, 682636, 5639688, 46590712, 384898384, 3179752720][n], 14*a(n-1) - 62*a(n-2) + 148*a(n-3) - 264*a(n-4) + 336*a(n-5) - 256*a(n-6) + 128*a(n-7) - 64*a(n-8) ));

/* Joerg Arndt, Aug 31 2012 */

(MAGMA)

m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(2*(1-6*x+22*x^2-52*x^3+34*x^4+92*x^5-222*x^6+184*x^7-24*x^8-64*x^10)/ (1-14*x+62*x^2-148*x^3+264*x^4-336*x^5+256*x^6-128*x^7+64*x^8)));

// Bruno Berselli, Sep 02 2012

CROSSREFS

Sequence in context: A056662 A151402 A199565 * A214767 A300412 A024915

Adjacent sequences:  A003765 A003766 A003767 * A003769 A003770 A003771

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 18 15:55 EST 2018. Contains 317323 sequences. (Running on oeis4.)