A166444 a(0) = 0, a(1) = 1 and for n > 1, a(n) = sum of all previous terms.

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, 4294967296, 8589934592

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

Inverse INVERT transform of A001519. - R. J. Mathar, Dec 08 2022

Links

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

Index entries for linear recurrences with constant coefficients, signature (2).

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

E.g.f.: (exp(2*x) + 2*x - 1)/4. - Stefano Spezia, Aug 07 2022

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 + ...

Maple

a:= n-> `if`(n<2, n, 2^(n-2)):
seq(a(n), n=0..40);  # Alois P. Heinz, Jun 02 2021

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: A120617 A131577 A155559 * A171449 A122803 A274867

Adjacent sequences: A166441 A166442 A166443 * A166445 A166446 A166447

Keyword

nonn,easy

Author

Robert G. Wilson v, Oct 13 2009

Status

approved