A215082 Related to Fibonacci numbers, see the Formula section.

0, 1, 1, 3, 4, 5, 8, 12, 17, 23, 35, 43, 66, 81, 124, 148, 229, 266, 414, 476, 742, 842, 1318, 1478, 2320, 2581, 4059, 4481, 7062, 7743, 12224, 13328, 21071, 22857, 36185, 39073, 61930, 66605, 105678, 113242, 179847, 192084, 305326, 325128, 517212, 549252

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

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).

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

Example

a(2) + a(3) = 2*2 = 4 -> a(3) = 3.
a(4) = a(3) + a(1) = 3 + 1 = 4.
a(4) + a(5) = 3*3 = 9 -> a(5) = 5.
a(6) = a(5) + a(3) = 5 + 3 = 8 , etc.

Maple

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

Crossrefs

Cf. A000045, A023607.

Sequence in context: A369575 A355158 A034403 * A320690 A179070 A358356

Adjacent sequences: A215079 A215080 A215081 * A215083 A215084 A215085

Keyword

nonn,easy

Author

Philippe Deléham, Aug 02 2012

Status

approved