A226538 a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.

1, 1, 2, 3, 4, 6, 7, 11, 12, 19, 20, 32, 33, 53, 54, 87, 88, 142, 143, 231, 232, 375, 376, 608, 609, 985, 986, 1595, 1596, 2582, 2583, 4179, 4180, 6763, 6764, 10944, 10945, 17709, 17710, 28655, 28656, 46366, 46367, 75023, 75024, 121391, 121392, 196416, 196417

Offset: 0

Author

V. T. Jayabalaji, Jun 10 2013

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,0,-1).

Programs

Haskell

a226538 n = a226538_list !! n
a226538_list = concat $ transpose [drop 2 a000071_list, tail a001911_list]
-- Reinhard Zumkeller, Jun 18 2013

Maple

f:= proc(n) option remember;
      if n <= 1 then 1
    elif n mod 2 = 0 then f(n-1)+1
    else f(n-1)+f(n-3)
      fi
    end:
t21:=[seq(f(n),n=0..60)];

Mathematica

LinearRecurrence[{0, 2, 0, 0, 0, -1}, {1, 1, 2, 3, 4, 6}, 50] (* Jean-François Alcover, Feb 13 2018 *)

Formula

a(2n) = A000071(n+3), a(2n+1) = A001911(n+1). - Philippe Deléham, Jun 18 2013

G.f.: (1+x+x^3)/((1-x)*(1+x)*(1-x^2-x^4)). - Philippe Deléham, Jun 18 2013

a(n) = a(n-1) + a(n-3)*(1-(-1)^n)/2 + (1+(-1)^n)/2. - Paolo P. Lava, Jun 27 2013

Extensions

Edited by N. J. A. Sloane, Jun 18 2013