OFFSET
1,2
COMMENTS
For more information see A206563.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Feb 17 2012
EXTENSIONS
More terms from Alois P. Heinz, Mar 12 2012
STATUS
approved