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A082958
Number of symmetric short bushes with n edges.
1
1, 0, 1, 1, 1, 2, 3, 4, 7, 10, 17, 25, 43, 64, 111, 167, 291, 442, 773, 1183, 2075, 3196, 5619, 8702, 15329, 23852, 42085, 65755, 116181, 182186, 322287, 507020, 897859, 1416594, 2510901, 3971887, 7045915, 11171924, 19832947, 31514404, 55982893
OFFSET
0,6
COMMENTS
Or number of ordered trees with n edges, no vertices of outdegree 1 and which are symmetrical with respect to the vertical axis passing through the root.
LINKS
F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999), 73-112.
FORMULA
G.f.: [(1-z)(1+z^2)-(1+z)sqrt(1-2z^2-3z^4)]/[2z(z^3+z^2+z-1)].
a(n) has antiparity of A007814(n+1), i.e. a(n) mod 2 = A035263(n+1). - Ralf Stephan, Feb 21 2004
D-finite with recurrence (n+1)*a(n) -2*a(n-1) +4*(-n+1)*a(n-2) +2*(-n+2)*a(n-3) +4*a(n-4) +2*(2*n-3)*a(n-5) +4*(2*n-11)*a(n-6) +6*(n-6)*a(n-7) +3*(n-7)*a(n-8)=0. - R. J. Mathar, Jul 24 2022
CROSSREFS
Sequence in context: A136570 A082766 A119016 * A218495 A166012 A060166
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 26 2003
STATUS
approved