A055365 Number of asymmetric mobiles (circular rooted trees) with n nodes and 4 leaves.

1, 5, 19, 53, 130, 280, 556, 1024, 1788, 2971, 4752, 7338, 11013, 16099, 23020, 32249, 44390, 60109, 80234, 105670, 137520, 176979, 225479, 284562, 356049, 441890, 544360, 665883, 809258, 977455, 1173871, 1402098, 1666212, 1970508, 2319825, 2719248, 3174469

Offset: 6

Author

Christian G. Bower, May 16 2000

Keywords

• nonn

Examples

			G.f. = x^6 + 5*x^7 + 19*x^8 + 53*x^9 + 130*x^10 + 280*x^11 + 556*x^12 + ...
		

Links

• Georg Fischer, Table of n, a(n) for n = 6..129
• Index entries for sequences related to mobiles

Crossrefs

Column 4 of A055363.

Cf. A055279.

Programs

PARI

{a(n) = if( n<6, n = -n; polcoeff( (1 + x + 3*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 5*x^6 + 2*x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) + x * O(x^n), n), n = n-6; polcoeff( (1 + 2*x + 5*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 3*x^6 + x^7 + x^8) / ((1 - x)^3 * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) + x * O(x^n), n))}; /* Michael Somos, Nov 02 2014 */

Formula

G.f.: x^6*( -1-2*x-5*x^2-5*x^3-7*x^4-5*x^5-3*x^6-x^7-x^8 ) / ( (x^2+1)*(1+x+x^2)*(1+x)^3*(x-1)^7 ). - R. J. Mathar, Sep 18 2011

a(5-n) = A055279(n) for all n in Z. - Michael Somos, Nov 02 2014

0 = -30 + a(n) - 2*a(n+1) - a(n+2) + 3*a(n+3) + a(n+5) - 2*a(n+6) - 2*a(n+7) + a(n+8) + 3*a(n+10) - a(n+11) - 2*a(n+12) + a(n+13) for all n in Z. - Michael Somos, Nov 02 2014

a(n) ~ n^6 / 1152 as n -> infinity. - Michael Somos, Nov 02 2014