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A166444 a(0) = 0, a(1) = 1 and for n > 1, a(n) = sum of all previous terms. 4
0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Essentially a duplicate of A000079. - N. J. A. Sloane, Oct 15 2009

a(n) is the number of compositions of n into an odd number of parts.

Also 0 together with A011782. - Omar E. Pol, Oct 28 2013

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..3317

FORMULA

a(n) = A000079(n-1) for n > 0.

O.g.f.: (x - x^2) / (1 - 2*x) = x / (1 - x / (1 - x)).

a(n) = (1-n) * a(n-1) + 2 * Sum_{k=1..n-1} a(k) * a(n-k) if n>1. - Michael Somos, Jul 23 2011

EXAMPLE

x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 16*x^6 + 32*x^7 + 64*x^8 + 128*x^9 + ...

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = Plus @@ Array[a, n - 1]; Array[a, 35, 0]

CROSSREFS

Cf. A000045, A000213, A000288, A000322, A000383, A011782, A034008, A060455, A123526, A127193, A127194, A127624, A131577, A163551.

Sequence in context: A034008 A123344 A141531 * A084633 A000079 A120617

Adjacent sequences:  A166441 A166442 A166443 * A166445 A166446 A166447

KEYWORD

easy,nonn

AUTHOR

Robert G. Wilson v, Oct 13 2009

STATUS

approved

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Last modified November 21 12:23 EST 2018. Contains 317449 sequences. (Running on oeis4.)