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 A184996 For each ordered partition of n with k numbers, remove 1 from each part and add the number k to get a new partition, until a partition is repeated. Among all ordered partitions of n, a(n) gives the maximum number of steps needed to reach a period. 1
 0, 1, 3, 5, 7, 8, 9, 11, 13, 15, 15, 16, 17, 22, 24, 24, 22, 23, 26, 33, 35, 35, 29, 30, 31, 38, 46, 48, 48, 41, 38, 39, 43, 52, 61, 63, 63, 55, 47, 48, 49, 58, 68, 78, 80, 80, 71, 62, 58, 59, 64, 75, 86, 97, 99, 99, 89, 79, 69, 70, 71, 82, 94, 106, 118, 120, 120, 109, 98, 87 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS If one plays with p(n,n) unordered partitions, one gets the same number and length of periods. If one removes the first part z(1) of each  partition and adds 1 to the next z(1) parts to get a new partition, until a partition is repeated, one gets the same length and number of periods, playing with 2^(n-1) ordered or p(n,n) unordered partitions (A185700, A092964, A037306) REFERENCES R. Baumann, Computer-Knobelei, LOGIN, 4 (1987), pages ?. H. R. Halder and W. Heise, Einführung in Kombinatorik, Hanser Verlag, Munich, 1976, pp. 75ff. LINKS FORMULA a((k^2+k-2)/2-j)=k^2-3-(k+1)*j with 0<=j<=(k-4) div 2 and 4<=k. a((k^2+k+2)/2+j)=k^2-1-k*j with 0<=j<=(k-5) div 2 and 5<=k. a((k^2+2*k-2+k mod 2)/2+j)=(k^2+4*k-2+k mod 2)/2+j with 0<=j<=2-k mod 2 and 4<=k. a(T(k))=k^2-1 with 1<= k  for all triangular numbers T(k). EXAMPLE For k=6: a(19)=26; a(20)=3; a(21)=35; a(22)=35; a(23)=29; a(24)=30; a(25)=31. For n=4: (1+1+1+1)->(4)->(3+1)->(2+2)->(1+1+2)->(1+3)--> a(4)=5 steps. For n=5: (1+1+1+1+1)->(5)->(4+1)->(3+2)->(2+1+2)->(1+1+3)->(2+3)->(1+2+2)--> a(5)=7 steps. CROSSREFS Cf. A185700, A092964, A037306. Sequence in context: A300737 A062958 A295075 * A153309 A047486 A229838 Adjacent sequences:  A184993 A184994 A184995 * A184997 A184998 A184999 KEYWORD nonn AUTHOR Paul Weisenhorn, Mar 28 2011 EXTENSIONS Partially edited by N. J. A. Sloane, Apr 08 2011 STATUS approved

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Last modified June 1 09:53 EDT 2020. Contains 334762 sequences. (Running on oeis4.)