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A166444
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a(0) = 0, a(1) = 1 and for n > 1, a(n) = sum of all previous terms.
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1
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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; internal format)
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OFFSET
| 0,4
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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.
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FORMULA
| a(n) = A000079(n-1) for n > 0.
O.g.f.: (x - x^2) / (1 - 2*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
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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 + ...
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MATHEMATICA
| a[0] = 0; a[1] = 1; a[n_] := a[n] = Plus @@ Array[a, n - 1]; Array[a, 35, 0]
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CROSSREFS
| Cf. A131577, A034008, A011782. Cf. A000045, A000213, A000288, A000322, A000383, A060455, A123526, A127193, A127194, A127624, A163551.
Sequence in context: A034008 A123344 A141531 * A084633 A122803 A000079
Adjacent sequences: A166441 A166442 A166443 * A166445 A166446 A166447
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KEYWORD
| easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 13 2009
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