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

%I A226538 #29 Feb 13 2018 04:02:24
%S A226538 1,1,2,3,4,6,7,11,12,19,20,32,33,53,54,87,88,142,143,231,232,375,376,
%T A226538 608,609,985,986,1595,1596,2582,2583,4179,4180,6763,6764,10944,10945,
%U A226538 17709,17710,28655,28656,46366,46367,75023,75024,121391,121392,196416,196417
%N A226538 a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.
%H A226538 Reinhard Zumkeller, <a href="/A226538/b226538.txt">Table of n, a(n) for n = 0..10000</a>
%H A226538 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,0,0,-1).
%F A226538 a(2n) = A000071(n+3), a(2n+1) = A001911(n+1). - _Philippe Deléham_, Jun 18 2013
%F A226538 G.f.: (1+x+x^3)/((1-x)*(1+x)*(1-x^2-x^4)). - _Philippe Deléham_, Jun 18 2013
%F A226538 a(n) = a(n-1) + a(n-3)*(1-(-1)^n)/2 + (1+(-1)^n)/2. - _Paolo P. Lava_, Jun 27 2013
%p A226538 f:= proc(n) option remember;
%p A226538       if n <= 1 then 1
%p A226538     elif n mod 2 = 0 then f(n-1)+1
%p A226538     else f(n-1)+f(n-3)
%p A226538       fi
%p A226538     end:
%p A226538 t21:=[seq(f(n),n=0..60)];
%t A226538 LinearRecurrence[{0, 2, 0, 0, 0, -1}, {1, 1, 2, 3, 4, 6}, 50] (* _Jean-François Alcover_, Feb 13 2018 *)
%o A226538 (Haskell)
%o A226538 a226538 n = a226538_list !! n
%o A226538 a226538_list = concat $ transpose [drop 2 a000071_list, tail a001911_list]
%o A226538 -- _Reinhard Zumkeller_, Jun 18 2013
%K A226538 nonn,easy
%O A226538 0,3
%A A226538 _V. T. Jayabalaji_, Jun 10 2013
%E A226538 Edited by _N. J. A. Sloane_, Jun 18 2013