# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a166444
Showing 1-1 of 1

%I A166444 #42 Jul 27 2024 09:40:50
%S A166444 0,1,1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,
%T A166444 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A166444 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592
%N A166444 a(0) = 0, a(1) = 1 and for n > 1, a(n) = sum of all previous terms.
%C A166444 Essentially a duplicate of A000079. - _N. J. A. Sloane_, Oct 15 2009
%C A166444 a(n) is the number of compositions of n into an odd number of parts.
%C A166444 Also 0 together with A011782. - _Omar E. Pol_, Oct 28 2013
%C A166444 Inverse INVERT transform of A001519. - _R. J. Mathar_, Dec 08 2022
%H A166444 Indranil Ghosh, <a href="/A166444/b166444.txt">Table of n, a(n) for n = 0..3317</a>
%H A166444 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F A166444 a(n) = A000079(n-1) for n > 0.
%F A166444 O.g.f.: x*(1 - x) / (1 - 2*x) = x / (1 - x / (1 - x)).
%F A166444 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
%F A166444 E.g.f.: (exp(2*x) + 2*x - 1)/4. - _Stefano Spezia_, Aug 07 2022
%e A166444 G.f. = x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 16*x^6 + 32*x^7 + 64*x^8 + 128*x^9 + ...
%p A166444 a:= n-> `if`(n<2, n, 2^(n-2)):
%p A166444 seq(a(n), n=0..40);  # _Alois P. Heinz_, Jun 02 2021
%t A166444 a[0] = 0; a[1] = 1; a[n_] := a[n] = Plus @@ Array[a, n - 1]; Array[a, 35, 0]
%o A166444 (Magma) [n le 1 select n else 2^(n-2): n in [0..40]]; // _G. C. Greubel_, Jul 27 2024
%o A166444 (SageMath) [(2^n +2*int(n==1) -int(n==0))/4 for n in range(41)] # _G. C. Greubel_, Jul 27 2024
%Y A166444 Cf. A000045, A000079, A000213, A000288, A000322, A000383, A001519.
%Y A166444 Cf. A011782, A034008, A060455, A123526, A127193, A127194, A127624.
%Y A166444 Cf. A131577, A163551.
%K A166444 nonn,easy
%O A166444 0,4
%A A166444 _Robert G. Wilson v_, Oct 13 2009

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE