The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A073708

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A073708

Generating function A(x) satisfies A(x) = (1+x)^2*A(x^2)^2, with A(0)=1.
(history; published version)

#17 by N. J. A. Sloane at Thu Apr 21 05:22:11 EDT 2016

STATUS

proposed

approved

#16 by Jean-François Alcover at Thu Apr 21 05:04:53 EDT 2016

STATUS

editing

proposed

#15 by Jean-François Alcover at Thu Apr 21 05:01:55 EDT 2016

MATHEMATICA

max = 38; f[x_] := Sum[ a[n]*x^n, {n, 0, max}]; coes = CoefficientList[ Series[f[x] - ((1 + x)*f[x^2])^2, {x, 0, max}], x]; sol = Solve[ Thread[coes == 0]]; A073708 = CoefficientList[ f[x] /. sol[[2]], x] (* Jean-François Alcover, Jan 04 2013 *)

A073708list[n_] := Module[{m = 1, A = 1}, While[m <= n, m = 2 m; A = ((1 + x)*(A /. x -> x^2))^2] + O[x]^m; CoefficientList[A, x][[1 ;; n]]]; A073708list[50] (* Jean-François Alcover, Apr 21 2016, adapted from PARI *)

STATUS

approved

editing

Discussion

Thu Apr 21

05:04

Jean-François Alcover: Removed my previous Mma script, which was far too slow.

#14 by Charles R Greathouse IV at Wed Apr 30 01:35:19 EDT 2014

EXTENSIONS

Edited by _Michael Somos, _, May 03, 2003

Discussion

Wed Apr 30

01:35

OEIS Server: https://oeis.org/edit/global/2180

#13 by Reinhard Zumkeller at Fri Jun 14 09:45:57 EDT 2013

STATUS

editing

approved

#12 by Reinhard Zumkeller at Thu Jun 13 13:25:59 EDT 2013

PROG

(Haskell)

a073708 n = a073708_list !! n

a073708_list = conv a073707_list [] where

conv (v:vs) ws = (sum $ zipWith (*) ws' $ reverse ws') : conv vs ws'

where ws' = v : ws

-- Reinhard Zumkeller, Jun 13 2013

STATUS

approved

editing

#11 by Paul D. Hanna at Fri Jan 04 18:00:31 EST 2013

STATUS

editing

approved

#10 by Paul D. Hanna at Fri Jan 04 18:00:29 EST 2013

EXTENSIONS

Edited by Paul D. Hanna, Jan 04 2013

STATUS

approved

editing

#9 by Paul D. Hanna at Fri Jan 04 17:56:21 EST 2013

STATUS

editing

approved

#8 by Paul D. Hanna at Fri Jan 04 17:56:12 EST 2013

LINKS

Paul D. Hanna, <a href="/A073708/b073708.txt">Table of n, a(n) for n = 0..1000</a>