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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
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.
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: A151402 A365526 A199565 * A214767 A300412 A333727
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009
STATUS
approved

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Last modified March 28 05:01 EDT 2024. Contains 371235 sequences. (Running on oeis4.)