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A206435
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Total sum of odd parts in the last section of the set of partitions of n.
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5
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1, 1, 5, 3, 13, 13, 29, 29, 66, 70, 126, 146, 241, 287, 450, 526, 791, 963, 1360, 1660, 2312, 2810, 3799, 4649, 6158, 7528, 9824, 11962, 15393, 18773, 23804, 28932, 36413, 44093, 54953, 66419, 82085, 98929, 121469, 145865, 177983, 213241, 258585, 308861
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OFFSET
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1,3
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COMMENTS
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a(n) is also the total sum of odd divisors of the terms in the n-th row of the triangle A336811.
a(n) is also the sum of odd terms in the n-th row of the triangle A207378.
a(n) is also the sum of odd terms in the n-th row of the triangle A336812. (End)
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LINKS
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FORMULA
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G.f.: (Sum_{i>=0} (2*i+1)*x^(2*i)*(1-x)/(1-x^(2*i+1))) / Product_{j>0} (1-x^j). - Alois P. Heinz, Mar 16 2012
a(n) ~ Pi * exp(Pi*sqrt(2*n/3)) / (24*sqrt(2*n)). - Vaclav Kotesovec, May 29 2018
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MAPLE
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b:= proc(n, i) option remember; local g, h;
if n=0 then [1, 0]
elif i<1 then [0, 0]
else g:= b(n, i-1); h:= `if`(i>n, [0, 0], b(n-i, i));
[g[1]+h[1], g[2]+h[2] +(i mod 2)*h[1]*i]
fi
end:
a:= n-> b(n, n)[2] -`if`(n=1, 0, b(n-1, n-1)[2]):
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MATHEMATICA
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b[n_, i_] := b[n, i] = Module[{g, h}, Which[n == 0, {1, 0}, i < 1, {0, 0}, True, g = b[n, i-1]; h = If[i > n, {0, 0}, b[n-i, i]]; {g[[1]] + h[[1]], g[[2]] + h[[2]] + Mod[i, 2]*h[[1]]*i}]]; a[n_] := b[n, n][[2]] - If[n == 1, 0, b[n-1, n-1][[2]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Feb 16 2017, after Alois P. Heinz *)
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CROSSREFS
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Cf. A000593, A002865, A135010, A138121, A138879, A206433, A206434, A206436, A207378, A336811, A336812.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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