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A168542 Number of trees that have a maximum 'n'. 4
1, 1, 1, 2, 2, 4, 5, 10, 10, 20, 25, 50, 52, 104, 130, 260, 260, 520, 650, 1300, 1352, 2704, 3380, 6760, 6770, 13540, 16925, 33850, 35204, 70408, 88010, 176020, 176020, 352040, 440050, 880100, 915304, 1830608, 2288260, 4576520, 4583290, 9166580, 11458225 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(2^n) = Product_{k=1..n} A003095(k). - Michael Somos, Dec 20 2018

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5654

FORMULA

a(1) = a(2) = 1, a(3*2^m + k) = A003095(m+2) * a(n - 2*2^m) where 0 <= k < 3*2^m. - Michael Somos, Dec 20 2018

a(n) = Sum_{k=0..n} (A309049(n,k)-A309049(n-1,k)) for n > 0, a(0) = 1. - Alois P. Heinz, Jul 12 2019

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, (g-> (f->

      1+b(f)*b(n-1-f))(min(g-1, n-g/2)))(2^ilog2(n)))

    end:

a:= n-> b(n)-`if`(n=0, 0, b(n-1)):

seq(a(n), n=0..45);  # Alois P. Heinz, Jul 12 2019

MATHEMATICA

a[ n_] := If[ n < 3, Boole[n > 0], With[{m = BitLength[Quotient[n, 3]] - 1}, Nest[#^2 + 1 &, 2, m] a[n - 2 2^m]]]; (* Michael Somos, Dec 20 2018 *)

PROG

(PARI) {a(n) = if( n<3, n>0, my(m = #binary(n\3)-1, t = 2); for(i=1, m, t = t^2+1); t*a(n - 2*2^m))}; /* Michael Somos, Dec 20 2018 */

CROSSREFS

Cf. A003095, A070939, A309049.

Partial differences of A091980. - Alois P. Heinz, Jul 12 2019

Sequence in context: A037026 A116651 A135586 * A116646 A306318 A091188

Adjacent sequences:  A168539 A168540 A168541 * A168543 A168544 A168545

KEYWORD

nonn

AUTHOR

Endi Begeja (andy.bege(AT)libero.it), Nov 29 2009

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jul 12 2019

STATUS

approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)