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A003746 Number of spanning trees with degrees 1 and 3 in O_5 X P_2n.

%I A003746 #15 Jan 01 2019 06:31:05
%S A003746 540,1751352,5386703316,16582103036544,51045000577926816,
%T A003746 157132783947988296192,483704801377335372564480,
%U A003746 1488997578825205151673656448,4583609224965381313988566950144
%N A003746 Number of spanning trees with degrees 1 and 3 in O_5 X P_2n.
%D A003746 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
%H A003746 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 A003746 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>
%H A003746 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>
%H A003746 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A003746 If b(n) denotes the number of spanning trees with degrees 1 and 3 in O_5 X P_n then
%F A003746 b(1) = 0,
%F A003746 b(2) = 540,
%F A003746 b(3) = 0,
%F A003746 b(4) = 1751352,
%F A003746 b(5) = 0,
%F A003746 b(6) = 5386703316,
%F A003746 b(7) = 0,
%F A003746 b(8) = 16582103036544,
%F A003746 b(9) = 0,
%F A003746 b(10) = 51045000577926816,
%F A003746 b(11) = 0,
%F A003746 b(12) = 157132783947988296192,
%F A003746 b(13) = 0,
%F A003746 b(14) = 483704801377335372564480,
%F A003746 b(15) = 0,
%F A003746 b(16) = 1488997578825205151673656448,
%F A003746 b(17) = 0,
%F A003746 b(18) = 4583609224965381313988566950144,
%F A003746 b(19) = 0,
%F A003746 b(20) = 14109810402621649533503234558344704,
%F A003746 b(21) = 0,
%F A003746 b(22) = 43434494483860386599671308650864330496,
%F A003746 b(23) = 0,
%F A003746 b(24) = 133705220498070622788909783421076412386304,
%F A003746 b(25) = 0,
%F A003746 b(26) = 411587292562609297454750726054600269987912704,
%F A003746 b(27) = 0,
%F A003746 b(28) = 1266996896366237649178359003459366628005457649664,
%F A003746 b(29) = 0,
%F A003746 b(30) = 3900220352788196660232362097608501848215326938755072,
%F A003746 b(31) = 0,
%F A003746 b(32) = 12006121596612176283154633057320394687803565435297505280,
%F A003746 b(33) = 0,
%F A003746 b(34) = 36958669704287162536274146164634194441880201040907341168640,
%F A003746 b(35) = 0,
%F A003746 b(36) = 113770567399219775084499535791661980035376168565367523333734400,
%F A003746 b(37) = 0,
%F A003746 b(38) = 350222075358923174025212352063864697242943327666094722900436582400,
%F A003746 b(39) = 0,
%F A003746 b(40) = 1078095195203820521745918151197065855397382661823414208194364252422144,
%F A003746 b(41) = 0,
%F A003746 b(42) = 3318720696661962582358070874565591095886422622888933137425721520537337856, and
%F A003746 b(n) = 2976b(n-2) + 311460b(n-4) + 10745408b(n-6) + 185361600b(n-8) - 11015685472b(n-10)
%F A003746 - 384432909824b(n-12) + 12586530486400b(n-14) - 142686379766272b(n-16) + 471457558327040b(n-18) + 3354655475796480b(n-20)
%F A003746 - 12936942677605376b(n-22) + 29721236628888576b(n-24) - 167487137019375616b(n-26) - 745271272714235904b(n-28) + 1043959728550182912b(n-30)
%F A003746 - 1512329782916284416b(n-32) + 206265260306202624b(n-34) + 59399388450127872b(n-36) + 26359905185169408b(n-38) + 154793410560000b(n-40).
%K A003746 nonn
%O A003746 1,1
%A A003746 _Frans J. Faase_
%E A003746 Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009