A055364 Number of asymmetric mobiles (circular rooted trees) with n nodes and 3 leaves.

1, 4, 10, 22, 42, 73, 119, 184, 272, 389, 540, 731, 969, 1261, 1614, 2037, 2538, 3126, 3811, 4603, 5512, 6550, 7728, 9058, 10553, 12226, 14090, 16160, 18450, 20975, 23751, 26794, 30120, 33747, 37692, 41973, 46609, 51619, 57022, 62839, 69090, 75796, 82979

Offset: 5

Author

Christian G. Bower, May 16 2000

Keywords

• nonn

Examples

			G.f. = x^5 + 4*x^6 + 10*x^7 + 22*x^8 + 42*x^9 + 73*x^10 + 119*x^11 + ...
		

Links

• Georg Fischer, Table of n, a(n) for n = 5..129
• Index entries for sequences related to mobiles
• Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,0,1,2,-3,1).

Crossrefs

Column 3 of A055363.

Cf. A055278.

Programs

Mathematica

a[ n_] := Quotient[ 3 n^4 - 28 n^3 + 102 n^2 - 180 n + 144, 144];

PARI

{a(n) = (3*n^4 - 28*n^3 + 102*n^2 - 180*n + 144) \ 144}; /* Michael Somos, Jun 29 2015 */

PARI

{a(n) = if( n<1, n = -n; polcoeff( (1 + x^2 + x^3) / ((1 - x)^3 * (1 - x^2) * (1 - x^3)) + x * O(x^n), n), polcoeff( x^5 * (1 + x + x^3) / ((1 - x)^3 * (1 - x^2) * (1 - x^3)) + x * O(x^n), n))}; /* Michael Somos, Jun 29 2015 */

Formula

G.f.: x^5*(x^3+x+1)/((1-x^2)*(1-x^3)*(1-x)^3).

a(n) = A055278(4 - n) for all n in Z. - Michael Somos, Jun 29 2015