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 A155861 a(n) is the smallest integer k such that the n-th (backward) difference of the partition sequence A000041 is positive from k onwards. 2
 1, 2, 8, 26, 68, 134, 228, 352, 510, 704, 934, 1204, 1514, 1866, 2260, 2702, 3188, 3722, 4304, 4936, 5620, 6354, 7140, 7980, 8872, 9822, 10826, 11888, 13006, 14182, 15416, 16712, 18066, 19480, 20956, 22494, 24096, 25760, 27486, 29278, 31134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Using a different (forward) definition of the difference operator, this sequence has also been given as 0,1,6,23,64,129,222,... A119712. LINKS Almkvist, Gert, On the differences of the partition function, Acta Arith., 61.2 (1992), 173-181. Knessl, Charles, Asymptotic Behavior of High-Order Differences of the Partition Function, Communications on Pure and Applied Mathematics, 44 (1991), 1033-1045. Odlyzko, A. M., Differences of the partition function, Acta Arith., 49 (1988), 237-254. Eric Weisstein's World of Mathematics, Backward Difference FORMULA An asymptotic formula is a(n) ~ 6/Pi^2 * n^2 (log n)^2. MAPLE A41:= n-> `if` (n<0, 0, combinat[numbpart](n)): DB:= proc(p)        proc(n) option remember;          p(n) -p(n-1)        end      end: a:= proc(n) option remember;       local f, k;       if n=0 then 1              else f:= (DB@@n)(A41);              for k from a(n-1) while not (f(k)>0 and f(k+1)>0) do od; k       fi     end: seq(a(n), n=0..20); CROSSREFS Cf. A000041, A002865, A053445, A072380, A081094, A081095, A175804, A119712. Sequence in context: A099416 A211885 A101696 * A212140 A136594 A268502 Adjacent sequences:  A155858 A155859 A155860 * A155862 A155863 A155864 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 16 2010 STATUS approved

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Last modified August 15 20:44 EDT 2018. Contains 313779 sequences. (Running on oeis4.)