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A003780 Number of spanning trees with degrees 1 and 3 in P_5 X P_n. 0

%I

%S 0,0,0,0,0,296,0,0,0,70420,0,0,0,16391166,0,0,0,3816021084,0,0,0,

%T 888375830566,0,0,0,206814474641944,0,0,0,48146529005876746,0,0,0,

%U 11208539472498838244,0,0,0,2609354391828066201746,0,0,0

%N Number of spanning trees with degrees 1 and 3 in P_5 X P_n.

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

%H F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

%H F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F Faase gives a 28-term linear recurrence on his web page:

%F a(1) = 0,

%F a(2) = 0,

%F a(3) = 0,

%F a(4) = 0,

%F a(5) = 0,

%F a(6) = 296,

%F a(7) = 0,

%F a(8) = 0,

%F a(9) = 0,

%F a(10) = 70420,

%F a(11) = 0,

%F a(12) = 0,

%F a(13) = 0,

%F a(14) = 16391166,

%F a(15) = 0,

%F a(16) = 0,

%F a(17) = 0,

%F a(18) = 3816021084,

%F a(19) = 0,

%F a(20) = 0,

%F a(21) = 0,

%F a(22) = 888375830566,

%F a(23) = 0,

%F a(24) = 0,

%F a(25) = 0,

%F a(26) = 206814474641944,

%F a(27) = 0,

%F a(28) = 0,

%F a(29) = 0,

%F a(30) = 48146529005876746,

%F a(31) = 0,

%F a(32) = 0,

%F a(33) = 0,

%F a(34) = 11208539472498838244,

%F a(35) = 0,

%F a(36) = 0,

%F a(37) = 0,

%F a(38) = 2609354391828066201746,

%F a(39) = 0,

%F a(40) = 0,

%F a(41) = 0,

%F a(42) = 607459192887167645884388,

%F a(43) = 0,

%F a(44) = 0,

%F a(45) = 0,

%F a(46) = 141416847085185500394182672,

%F a(47) = 0,

%F a(48) = 0,

%F a(49) = 0,

%F a(50) = 32921922778799648796216249818,

%F a(51) = 0,

%F a(52) = 0,

%F a(53) = 0,

%F a(54) = 7664242427921761934124201980862,

%F a(55) = 0,

%F a(56) = 0,

%F a(57) = 0,

%F a(58) = 1784240015038927382237215443432910 and

%F a(n) = 262a(n-4) - 7125a(n-8) + 78668a(n-12) - 581608a(n-16) + 2138065a(n-20)

%F - 5215246a(n-24) + 16969316a(n-28) - 43146455a(n-32) + 39514076a(n-36) + 7628882a(n-40)

%F - 6116529a(n-44) + 23336a(n-48) - 2876a(n-52) + 64a(n-56).

%K nonn

%O 1,6

%A _Frans J. Faase_

%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)