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

Author

Philippe Deléham, Aug 02 2012

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Cf. A000045, A023607.

Programs

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

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