A207381 Total sum of the odd-indexed parts of all partitions of n.

1, 3, 7, 14, 25, 45, 72, 117, 180, 275, 403, 596, 846, 1206, 1681, 2335, 3183, 4342, 5820, 7799, 10321, 13622, 17798, 23221, 30009, 38706, 49567, 63316, 80366, 101805, 128211, 161134, 201537, 251495, 312508, 387535, 478674, 590072, 724920, 888795, 1086324

Offset: 1

Author

Omar E. Pol, Feb 17 2012

Keywords

• nonn

Comments

For more information see A206563.

Examples

			For n = 5, write the partitions of 5 and below write the sums of their odd-indexed parts:
.    5
.    3+2
.    4+1
.    2+2+1
.    3+1+1
.    2+1+1+1
.    1+1+1+1+1
.  ------------
.   20 + 4 + 1 = 25
The total sum of the odd-indexed parts is 25 so a(5) = 25.
		

Links

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

Crossrefs

Cf. A066186, A066897, A066898, A181187, A194714, A206283, A206563, A207031, A207032, A207382.

Programs

Maple

b:= proc(n, i) option remember; local g, h;
      if n=0 then [1, 0$2]
    elif i<1 then [0$3]
    else g:= b(n, i-1); h:= `if`(i>n, [0$3], b(n-i, i));
         [g[1]+h[1], g[2]+h[3], g[3]+h[2]+i*h[1]]
      fi
    end:
a:= n-> b(n,n)[3]:
seq(a(n), n=1..50); # Alois P. Heinz, Mar 12 2012

Mathematica

b[n_, i_] := b[n, i] = Module[{g, h}, If[n == 0 , {1, 0, 0}, If[i < 1, {0, 0, 0},  g = b[n, i - 1]; h = If[i > n, {0, 0, 0}, b[n - i, i]]; {g[[1]] + h[[1]], g[[2]] + h[[3]], g[[3]] + h[[2]] + i*h[[1]]}]]]; a[n_] := b[n, n][[3]]; Table [a[n], {n, 1, 50}] (* Jean-François Alcover, Dec 09 2016 after Alois P. Heinz *)

Formula

a(n) = A066186(n) - A207382(n) = A066897(n) + A207382(n).

Extensions

More terms from Alois P. Heinz, Mar 12 2012