A055365 - OEIS

%I #18 Mar 16 2022 05:54:22

%S 1,5,19,53,130,280,556,1024,1788,2971,4752,7338,11013,16099,23020,

%T 32249,44390,60109,80234,105670,137520,176979,225479,284562,356049,

%U 441890,544360,665883,809258,977455,1173871,1402098,1666212,1970508,2319825,2719248,3174469

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

%H Georg Fischer, <a href="/A055365/b055365.txt">Table of n, a(n) for n = 6..129</a>

%H <a href="/index/Mo#mobiles">Index entries for sequences related to mobiles</a>

%F 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

%F a(5-n) = A055279(n) for all n in Z. - _Michael Somos_, Nov 02 2014

%F 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

%F a(n) ~ n^6 / 1152 as n -> infinity. - _Michael Somos_, Nov 02 2014

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

%o (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 */

%Y Column 4 of A055363.

%Y Cf. A055279.

%K nonn

%O 6,2

%A _Christian G. Bower_, May 16 2000