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A055364 Number of asymmetric mobiles (circular rooted trees) with n nodes and 3 leaves. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,2
LINKS
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
EXAMPLE
G.f. = x^5 + 4*x^6 + 10*x^7 + 22*x^8 + 42*x^9 + 73*x^10 + 119*x^11 + ...
MATHEMATICA
a[ n_] := Quotient[ 3 n^4 - 28 n^3 + 102 n^2 - 180 n + 144, 144];
PROG
(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 */
CROSSREFS
Column 3 of A055363.
Cf. A055278.
Sequence in context: A188281 A227327 A023609 * A284870 A032191 A065568
KEYWORD
nonn
AUTHOR
Christian G. Bower, May 16 2000
STATUS
approved

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Last modified May 26 13:56 EDT 2024. Contains 372826 sequences. (Running on oeis4.)