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 A215082 Related to Fibonacci numbers, see the Formula section. 4

%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(2n-1) + a(2n-3).

%F G.f.: x*(2*x^2+1)*(x^3+x+1) / ((x^2-x+1)*(x^2+x+1)*(x^4+x^2-1)^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=j-1, 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

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Last modified December 6 20:22 EST 2021. Contains 349567 sequences. (Running on oeis4.)