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

1,2

Comments

Suggested by A006336, A007604 and A249036-A249038.

Links

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

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

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

Prog

(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

Crossrefs

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

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

Sequence in context: A194805 A084842 A289177 * A342492 A280962 A096967

Adjacent sequences: A249036 A249037 A249038 * A249040 A249041 A249042

Keyword

nonn

Author

N. J. A. Sloane, Oct 26 2014

Status

approved