The On-Line Encyclopedia of Integer Sequences (OEIS)

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A067353

Divide the natural numbers in sets of consecutive numbers starting with {1,2} as the first set. The number of elements of the n-th set is equal to the sum of the n-1 final numbers in the (n-1)st set. The final number of the n-th set gives a(n).
(history; published version)

#10 by N. J. A. Sloane at Mon Mar 02 16:08:48 EST 2015

AUTHOR

_Floor van Lamoen (fvlamoen(AT)hotmail.com), _, Jan 17 2002

Discussion

Mon Mar 02

16:08

OEIS Server: https://oeis.org/edit/global/2352

#9 by Joerg Arndt at Mon May 06 09:17:56 EDT 2013

STATUS

editing

approved

#8 by Joerg Arndt at Mon May 06 09:17:13 EDT 2013

FORMULA

E.g.f. (with a(0)=2): (exp(x)*(x^2-2*x+2)-6)/(2*(x-1)). - Vaclav Kotesovec, Oct 21 2012

PROG

(PARI) x='x+O('x^66); Vec(serlaplace((exp(x)*(x^2-2*x+2)-6)/(2*(x-1))) -2 ) \\ Joerg Arndt, May 06 2013

STATUS

proposed

editing

#7 by Vincenzo Librandi at Mon May 06 09:12:49 EDT 2013

STATUS

editing

proposed

#6 by Vincenzo Librandi at Mon May 06 09:12:36 EDT 2013

DATA

2, 4, 11, 41, 199, 1184, 8273, 66163, 595439, 5954354, 65497849, 785974133, 10217663663, 143047291204, 2145709367969, 34331349887399, 583632948085663, 10505393065541798, 199602468245294009, 3992049364905880009, 83833036663023479999

LINKS

Vincenzo Librandi, <a href="/A067353/b067353.txt">Table of n, a(n) for n = 1..200</a>

EXTENSIONS

More terms from Vincenzo Librandi, May 06 2013

STATUS

approved

editing

#5 by T. D. Noe at Sun Oct 21 14:34:42 EDT 2012

STATUS

proposed

approved

#4 by Vaclav Kotesovec at Sun Oct 21 14:18:49 EDT 2012

STATUS

editing

proposed

#3 by Vaclav Kotesovec at Sun Oct 21 14:18:45 EDT 2012

FORMULA

E.g.f.: (exp(x)*(x^2-2*x+2)-6)/(2*(x-1)). - Vaclav Kotesovec, Oct 21 2012

MATHEMATICA

Rest[CoefficientList[Series[(E^x*(x^2-2*x+2)-6)/(2*(x-1)), {x, 0, 20}], x]*Range[0, 20]!] (* Vaclav Kotesovec, Oct 21 2012 *)

STATUS

approved

editing

#2 by N. J. A. Sloane at Tue Jan 24 03:00:00 EST 2006

KEYWORD

easy,nonn,new

AUTHOR

Floor van Lamoen (f_DOT_v_DOT_lamoen_fvlamoen(AT_wxs_DOT_nl), hotmail.com), Jan 17 2002

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

NAME

Divide the natural numbers in sets of consecutive numbers starting with {1,2} as the first set. The number of elements of the n-th set is equal to the sum of the n-1 final numbers in the (n-1)st set. The final number of the n-th set gives a(n).

DATA

2, 4, 11, 41, 199, 1184, 8273, 66163, 595439, 5954354, 65497849, 785974133, 10217663663, 143047291204, 2145709367969, 34331349887399, 583632948085663

OFFSET

1,1

FORMULA

a(n)=n*a(n-1)-(n-1)(n-2)/2 with a(1)=2. a(n)=b(1)+b(2)+...+b(n) with b(n) as in A067352.

EXAMPLE

The sets begin {1,2},{3,4},{5,6,...,9,10,11},{12,13,...,38,39,40,41},...

KEYWORD

easy,nonn

AUTHOR

Floor van Lamoen (f_DOT_v_DOT_lamoen_AT_wxs_DOT_nl), Jan 17 2002

STATUS

approved