A249039 a(1)=1, a(2)=2; thereafter a(n) = a(n-1) + a(n-1-(number of even terms so far)) + a(n-1-(number of odd terms so far)).

1, 2, 4, 7, 11, 17, 26, 37, 52, 70, 92, 120, 157, 200, 254, 323, 401, 490, 597, 719, 859, 1021, 1211, 1438, 1687, 1979, 2325, 2740, 3183, 3704, 4262, 4863, 5553, 6350, 7201, 8174, 9216, 10336, 11545, 12894, 14350, 15928, 17646, 19526, 21596, 23893, 26352, 29060, 32060, 35406, 39167

Offset: 1

Author

N. J. A. Sloane, Oct 26 2014

Keywords

• nonn

Comments

Suggested by A006336, A007604 and A249036-A249038.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006336, A007604, A249036, A249037, A249038.

A249040 and A249041 give numbers of even and odd terms so far.

Programs

Haskell

import Data.List (genericIndex)
a249039 n = genericIndex a249039_list (n - 1)
a249039_list = 1 : 2 : f 2 2 1 1 where
   f x u v w = y : f (x + 1) y (v + 1 - mod y 2) (w + mod y 2)
               where y = u + a249039 (x - v) + a249039 (x - w)
-- Reinhard Zumkeller, Nov 11 2014

Maple

M:=100;
v[1]:=1; v[2]:=2; w[1]:=0; w[2]:=1; x[1]:=1; x[2]:=1;
for n from 3 to M do
v[n]:=v[n-1]+v[n-1-w[n-1]]+v[n-1-x[n-1]];
if v[n] mod 2 = 0 then w[n]:=w[n-1]+1; x[n]:=x[n-1];
else w[n]:=w[n-1]; x[n]:=x[n-1]+1; fi;
od:
[seq(v[n], n=1..M)]; # A249039
[seq(w[n], n=1..M)]; # A249040
[seq(x[n], n=1..M)]; # A249041

Formula

For n > 1: a(n+1) = a(n) + a(n - A249040(n)) + a(n - A249041(n)) by mutual recursion. - Reinhard Zumkeller, Nov 11 2014