A206433 Total number of odd parts in the last section of the set of partitions of n.

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

Alois P. Heinz, Table of n, a(n) for n = 1..1000

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 *)

Crossrefs

Partial sums give A066897.

Cf. A001227, A002865, A006128, A135010, A138121, A138137, A182703, A206434, A206435, A206436, A207378, A336811, A336812.

Sequence in context: A360875 A131036 A331788 * A301589 A237666 A285187

Adjacent sequences: A206430 A206431 A206432 * A206434 A206435 A206436

Keyword

nonn

Author

Omar E. Pol, Feb 12 2012

Extensions

More terms from Alois P. Heinz, Mar 22 2012

Status

approved