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A206433
Total number of odd parts in the last section of the set of partitions of n.
4
1, 1, 3, 3, 7, 9, 15, 19, 32, 40, 60, 78, 111, 143, 200, 252, 343, 437, 576, 728, 952, 1190, 1531, 1911, 2426, 3008, 3788, 4664, 5819, 7143, 8830, 10780, 13255, 16095, 19661, 23787, 28881, 34795, 42051, 50445, 60675, 72547, 86859, 103481, 123442, 146548
OFFSET
1,3
COMMENTS
From Omar E. Pol, Apr 07 2023: (Start)
Convolution of A002865 and A001227.
a(n) is also the total number of odd divisors of the terms in the n-th row of the triangle A336811.
a(n) is also the number of odd terms in the n-th row of the triangle A207378.
a(n) is also the number of odd terms in the n-th row of the triangle A336812. (End)
LINKS
MAPLE
b:= proc(n, i) option remember; local f, g;
if n=0 or i=1 then [1, n]
else f:= b(n, i-1); g:= `if`(i>n, [0, 0], b(n-i, i));
[f[1]+g[1], f[2]+g[2]+ (i mod 2)*g[1]]
fi
end:
a:= n-> b(n, n)[2] -b(n-1, n-1)[2]:
seq(a(n), n=1..50); # Alois P. Heinz, Mar 22 2012
MATHEMATICA
b[n_, i_] := b[n, i] = Module[{f, g}, If[n==0 || i==1, {1, n}, f = b[n, i-1]; g = If[i>n, {0, 0}, b[n-i, i]]; {f[[1]]+g[[1]], f[[2]]+g[[2]] + Mod[i, 2]*g[[1]]}]]; a[n_] := b[n, n][[2]]-b[n-1, n-1][[2]]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Feb 16 2017, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 12 2012
EXTENSIONS
More terms from Alois P. Heinz, Mar 22 2012
STATUS
approved