来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a036652 Showing 1-1 of 1 %I A036652 %S A036652 0,0,1,0,1,1,3,4,11,19,49,103,254,583,1445,3506,8815,22082,56286, %T A036652 143822,371354,963250,2516822,6607348,17440933,46233833,123090070, %U A036652 328923702,882114742,2373351473,6405275496,17336081498,47047112028 %N A036652 Number of bicentered 6-valent trees with n nodes. %H A036652 E. M. Rains and N. J. A. Sloane,关于Cayle对烷烃(或四价树)的计数。J.整数序列,第2卷(1999),第91.1.1页,第0%H A036652与树相关的序列的索引条目%H A036652 E. M. Rains和N.J.A.斯隆,关于Cayle对烷烃(或四价树)的计数, J. Integer Sequences, Vol. 2 (1999), Article 99.1.1. %t A036652 n = 20; (* algorithm from Rains and Sloane *) %t A036652 S5[f_,h_,x_] := f[h,x]^5/120 + f[h,x]^3 f[h,x^2]/12 + f[h,x]^2 f[h,x^3]/6 + f[h,x] f[h,x^2]^2/8 + f[h,x] f[h,x^4]/4 + f[h,x^2] f[h,x^3]/6 + f[h,x^5]/5; %t A036652 T[-1,z_] := 1; T[h_,z_] := T[h,z] = Table[z^k, {k,0,n}].Take[CoefficientList[z^(n+1) + 1 + S5[T,h-1,z]z, z], n+1]; %t A036652 Sum[Take[CoefficientList[z^(n+1) + (T[h,z] - T[h-1,z])^2/2 + (T[h,z^2] - T[h-1,z^2])/2, z],n+1], {h,0,n/2}] (* _Robert A. Russell_, Sep 15 2018 *) %Y A036652 A036652 = A036653 - A036651. %K A036652 nonn %O A036652 0,7 %A A036652 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE