The On-Line Encyclopedia of Integer Sequences (OEIS)

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A084080

Length of lists created by n substitutions k -> Range[k+1,1,-3] starting with {1}, counting down from k+1 to 1 step -3.
(history; published version)

#6 by Russ Cox at Fri Mar 30 18:58:50 EDT 2012

COMMENTS

Would appear to coincide with row sums of the inverse of the Riordan array (1-x^3,x(1-x^3)). These row sums have g.f. 1/(1-y-y^3+y^4) where y^4-y+x=0. - _Paul Barry (pbarry(AT)wit.ie), _, May 10 2005

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/287

#5 by Russ Cox at Fri Mar 30 18:37:43 EDT 2012

AUTHOR

_Wouter Meeussen (wouter.meeussen(AT)pandora.be), _, May 11 2003

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/214

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

CROSSREFS

Cf. A124753.

KEYWORD

nonn,new

nonn

#3 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

MATHEMATICA

Length/@Flatten/@NestList[ # /. k_Integer:>Range[k+1, 1, -3]&, {1}, 21]

KEYWORD

nonn,new

nonn

#2 by N. J. A. Sloane at Tue Jul 19 03:00:00 EDT 2005

DATA

1, 1, 1, 2, 3, 4, 9, 15, 22, 52, 91, 140, 340, 612, 969, 2394, 4389, 7084, 17710, 32890, 53820, 135720, 254475, 420732, 1068012, 2017356, 3362260, 8579560, 16301164, 27343888, 70068713

COMMENTS

Would appear to coincide with row sums of the inverse of the Riordan array (1-x^3,x(1-x^3)). These row sums have g.f. 1/(1-y-y^3+y^4) where y^4-y+x=0. - Paul Barry (pbarry(AT)wit.ie), May 10 2005

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Fri May 16 03:00:00 EDT 2003

NAME

Length of lists created by n substitutions k -> Range[k+1,1,-3] starting with {1}, counting down from k+1 to 1 step -3.

DATA

1, 1, 1, 2, 3, 4, 9, 15, 22, 52, 91, 140, 340, 612, 969, 2394, 4389, 7084, 17710, 32890, 53820, 135720

OFFSET

0,4

EXAMPLE

{1}, {2}, {3}, {4, 1}, {5, 2, 2}, {6, 3, 3, 3}, {7, 4, 1, 4, 1, 4, 1, 4, 1}

MATHEMATICA

Length/@Flatten/@NestList[ # /. k_Integer:>Range[k+1, 1, -3]&, {1}, 21]

KEYWORD

nonn,new

AUTHOR

Wouter Meeussen (wouter.meeussen(AT)pandora.be), May 11 2003

STATUS

approved