|
|
FORMULA
| If b(n) denotes the number of spanning trees with degrees 1 and 3 in O_5 X P_n then
b(1) = 0,
b(2) = 540,
b(3) = 0,
b(4) = 1751352,
b(5) = 0,
b(6) = 5386703316,
b(7) = 0,
b(8) = 16582103036544,
b(9) = 0,
b(10) = 51045000577926816,
b(11) = 0,
b(12) = 157132783947988296192,
b(13) = 0,
b(14) = 483704801377335372564480,
b(15) = 0,
b(16) = 1488997578825205151673656448,
b(17) = 0,
b(18) = 4583609224965381313988566950144,
b(19) = 0,
b(20) = 14109810402621649533503234558344704,
b(21) = 0,
b(22) = 43434494483860386599671308650864330496,
b(23) = 0,
b(24) = 133705220498070622788909783421076412386304,
b(25) = 0,
b(26) = 411587292562609297454750726054600269987912704,
b(27) = 0,
b(28) = 1266996896366237649178359003459366628005457649664,
b(29) = 0,
b(30) = 3900220352788196660232362097608501848215326938755072,
b(31) = 0,
b(32) = 12006121596612176283154633057320394687803565435297505280,
b(33) = 0,
b(34) = 36958669704287162536274146164634194441880201040907341168640,
b(35) = 0,
b(36) = 113770567399219775084499535791661980035376168565367523333734400,
b(37) = 0,
b(38) = 350222075358923174025212352063864697242943327666094722900436582400,
b(39) = 0,
b(40) = 1078095195203820521745918151197065855397382661823414208194364252422144,
b(41) = 0,
b(42) = 3318720696661962582358070874565591095886422622888933137425721520537337856, and
b(n) = 2976b(n-2) + 311460b(n-4) + 10745408b(n-6) + 185361600b(n-8) - 11015685472b(n-10)
- 384432909824b(n-12) + 12586530486400b(n-14) - 142686379766272b(n-16) + 471457558327040b(n-18) + 3354655475796480b(n-20)
- 12936942677605376b(n-22) + 29721236628888576b(n-24) - 167487137019375616b(n-26) - 745271272714235904b(n-28) + 1043959728550182912b(n-30)
- 1512329782916284416b(n-32) + 206265260306202624b(n-34) + 59399388450127872b(n-36) + 26359905185169408b(n-38) + 154793410560000b(n-40).
|
