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A155861
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a(n) is the smallest integer k such that the n-th (backward) difference of the partition sequence A000041 is positive from k onwards.
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3
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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
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OFFSET
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0,2
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COMMENTS
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Using a different (forward) definition of the difference operator, this sequence has also been given as 0, 1, 6, 23, 64, 129, 222, ... A119712.
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LINKS
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FORMULA
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An asymptotic formula is a(n) ~ 6/Pi^2 * n^2 (log n)^2.
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MAPLE
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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);
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MATHEMATICA
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a[n_] := a[n] = Module[{f}, f[i_] = DifferenceDelta[PartitionsP[i], {i, n}]; For[j = 2, True, j++, If[f[j] > 0 && f[j + 1] > 0, Return[j + n]]]];
a[0] = 1; a[1] = 2;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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