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A079798
Partition of positive integers into shortest possible groups, starting with (1), (2,3), (4,5,6), (7,8,9,10,11), such that a(n) = the sum of the terms of the n-th group is a multiple of a(n-1) and a(n) > a(n-1).
5
1, 5, 15, 45, 495, 16830, 4358970, 1159486020, 196818113950920, 3151092455396895169036800, 136084696980410308844836382925537725529600, 9996588705394796239042140065772174939073840705818917941136700639014745600
OFFSET
1,2
COMMENTS
Dropping requirement a(n) > a(n-1) leads to a different partition: (1), (2, 3), (4, 5, 6), (7, 8), ... - see A160275.
For partition starting with (1), (2), (3,4,5), see A075631.
FORMULA
a(n) = A000217(A079801(n)) - A000217(A079801(n-1)) [From R. J. Mathar and Max Alekseyev]
PROG
(PARI) A000217(n)= { return(n*(n+1)/2) ; } upto(first, osum, strict)= { local(trifirst, tstsu) ; trifirst=A000217(first-1) ; for(lst=first+1, first+100000000, tstsu=A000217(lst)-trifirst ; if(strict==1 && tstsu<= osum, next ; ) ; if( tstsu % osum == 0, return(lst) ; ) ; ) ; return(-1) ; } { a=1 ; first=2 ; for(n=2, 40, last=upto(first, a, 1) ; a=A000217(last)-A000217(first-1) ; print(a, ", ") ; first=last+1 ; ) ; - R. J. Mathar, May 06 2006
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Feb 05 2003
EXTENSIONS
More terms from R. J. Mathar, May 06 2006
Edited and extended by Max Alekseyev, May 08 2009
STATUS
approved