The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A103419

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A103419

Number of compositions of n in which the least part is odd.
(history; published version)

#14 by Alois P. Heinz at Sun Jul 26 14:03:08 EDT 2015

STATUS

editing

approved

#13 by Alois P. Heinz at Sun Jul 26 14:03:00 EDT 2015

LINKS

Alois P. Heinz, <a href="/A103419/b103419.txt">Table of n, a(n) for n = 1..1000</a>

MAPLE

b:= proc(n, i) option remember; `if`(n=0, irem(i, 2), add(

(t-> b(t, min(i, j, `if`(t>0, t, j))))(n-j), j=1..n))

end:

a:= n-> b(n$2):

seq(a(n), n=0..40); # Alois P. Heinz, Jul 26 2015

#12 by Alois P. Heinz at Sun Jul 26 13:38:03 EDT 2015

DATA

1, 1, 4, 6, 14, 28, 59, 117, 239, 484, 980, 1973, 3973, 7989, 16054, 32227, 64653, 129628, 259787, 520440, 1042305, 2086938, 4177680, 8361557, 16733221, 33482909, 66992641, 134028938, 268128902, 536373288, 1072934271, 2146173471, 4292842170, 8586488355

STATUS

approved

editing

#11 by Jon E. Schoenfield at Sun Mar 29 14:11:29 EDT 2015

STATUS

editing

approved

#10 by Jon E. Schoenfield at Sun Mar 29 14:11:26 EDT 2015

MATHEMATICA

Rest[ CoefficientList[ Series[ Expand[ Sum[(1 - x)^2*x^(2n - 1)/((1 - x - x^(2n))*(1 - x - x^(2n - 1))), {n, 35}]], {x, 0, 35}], x]] (from * _Robert G. Wilson v _, Feb 05 2005 *)

STATUS

approved

editing

#9 by Vaclav Kotesovec at Thu May 01 17:08:23 EDT 2014

STATUS

editing

approved

#8 by Vaclav Kotesovec at Thu May 01 17:07:41 EDT 2014

FORMULA

a(n) ~ 2^(n-1). - Vaclav Kotesovec, May 01 2014

STATUS

approved

editing

#7 by Charles R Greathouse IV at Fri May 10 12:45:40 EDT 2013

FORMULA

G.f.: Sum(x^k/((1-x)^k*(1+x^k)),k=1..infinity). - _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Mar 02 2008

AUTHOR

_Vladeta Jovovic (vladeta(AT)eunet.rs), _, Feb 04 2005

Discussion

Fri May 10

12:45

OEIS Server: https://oeis.org/edit/global/1911

#6 by Russ Cox at Fri Mar 30 17:31:11 EDT 2012

EXTENSIONS

More terms from _Robert G. Wilson v (rgwv(AT)rgwv.com), _, Feb 05 2005

Discussion

Fri Mar 30

17:31

OEIS Server: https://oeis.org/edit/global/156

#5 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

FORMULA

G.f.: Sum(x^k/((1-x)^k*(1+x^k)),k=1..infinity). - Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Mar 02 2008

KEYWORD

easy,nonn,new

AUTHOR

Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Feb 04 2005