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A309840 If n = Sum (2^e_k) then a(n) = Product (Fibonacci(e_k + 3)). 0
1, 2, 3, 6, 5, 10, 15, 30, 8, 16, 24, 48, 40, 80, 120, 240, 13, 26, 39, 78, 65, 130, 195, 390, 104, 208, 312, 624, 520, 1040, 1560, 3120, 21, 42, 63, 126, 105, 210, 315, 630, 168, 336, 504, 1008, 840, 1680, 2520, 5040, 273, 546, 819, 1638, 1365, 2730, 4095, 8190 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..55.

FORMULA

G.f.: Product_{k>=0} (1 + Fibonacci(k + 3) * x^(2^k)).

a(0) = 1; a(n) = Fibonacci(floor(log_2(n)) + 3) * a(n - 2^floor(log_2(n))).

a(2^(k-2)-1) = A003266(k).

EXAMPLE

23 = 2^0 + 2^1 + 2^2 + 2^4 so a(23) = Fibonacci(3) * Fibonacci(4) * Fibonacci(5) * Fibonacci(7) = 390.

MATHEMATICA

nmax = 55; CoefficientList[Series[Product[(1 + Fibonacci[k + 3] x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]

a[0] = 1; a[n_] := Fibonacci[Floor[Log[2, n]] + 3] a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 55}]

PROG

(PARI) a(n)={vecprod([fibonacci(k+2) | k<-Vec(select(b->b, Vecrev(digits(n, 2)), 1))])} \\ Andrew Howroyd, Aug 19 2019

CROSSREFS

Cf. A000045, A003266, A019565, A022290, A029930, A121663, A160009.

Sequence in context: A239956 A077320 A019565 * A274608 A319680 A133477

Adjacent sequences:  A309837 A309838 A309839 * A309841 A309842 A309843

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Aug 19 2019

STATUS

approved

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Last modified April 2 19:05 EDT 2020. Contains 333190 sequences. (Running on oeis4.)