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A215082 Related to Fibonacci numbers, see the Formula section. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A327182 A030403 A034403 * A320690 A179070 A039020

Adjacent sequences:  A215079 A215080 A215081 * A215083 A215084 A215085

KEYWORD

nonn,easy

AUTHOR

Philippe Deléham, Aug 02 2012

STATUS

approved

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Last modified October 23 00:39 EDT 2021. Contains 348211 sequences. (Running on oeis4.)