%I
%S 0,1,1,3,4,5,8,12,17,23,35,43,66,81,124,148,229,266,414,476,742,842,
%T 1318,1478,2320,2581,4059,4481,7062,7743,12224,13328,21071,22857,
%U 36185,39073,61930,66605,105678,113242,179847,192084,305326,325128,517212,549252
%N Related to Fibonacci numbers, see the Formula section.
%H Alois P. Heinz, <a href="/A215082/b215082.txt">Table of n, a(n) for n = 0..1000</a>
%F a(0) = 0, a(1) = 1, a(2) = 1, a(2n) + a(2n+1) = (n+1)*Fibonacci(n+2), a(2n) = a(2n1) + a(2n3).
%F G.f.: x*(2*x^2+1)*(x^3+x+1) / ((x^2x+1)*(x^2+x+1)*(x^4+x^21)^2).  _Alois P. Heinz_, Aug 02 2012
%e a(2) + a(3) = 2*2 = 4 > a(3) = 3.
%e a(4) = a(3) + a(1) = 3 + 1 = 4.
%e a(4) + a(5) = 3*3 = 9 > a(5) = 5.
%e a(6) = a(5) + a(3) = 5 + 3 = 8 , etc.
%p a:= n> (Matrix(6, (i, j)> `if`(i=j1, 1, `if`(i=6, [1, 3, 2, 1, 2, 1][j], 0)))^iquo(n, 2, 'r'). `if`(r=0, <<0, 1, 4, 8, 17, 35>>, <<1, 3, 5, 12, 23, 43>>))[1, 1]: seq (a(n), n=0..50); # _Alois P. Heinz_, Aug 02 2012
%Y Cf. A000045, A023607.
%K nonn,easy
%O 0,4
%A _Philippe Deléham_, Aug 02 2012
