A160424 - OEIS

%I #15 Feb 24 2021 02:48:18

%S 0,1,4,11,22,37,60,95,138,185,240,307,386,481,604,759,930,1105,1288,

%T 1483,1690,1913,2164,2447,2750,3069,3416,3799,4222,4705,5276,5927,

%U 6610,7297,7992,8699,9418,10153,10916,11711,12526,13357,14216,15111,16046,17041,18124

%N Partial sums of A139250.

%H N. J. A. Sloane, <a href="/A160424/b160424.txt">Table of n, a(n) for n = 0..65535</a>

%H David Applegate, Omar E. Pol and N. J. A. Sloane, <a href="/A000695/a000695_1.pdf">The Toothpick Sequence and Other Sequences from Cellular Automata</a>, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.]

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%F G.f.: (x/((1-x)^2*(1+2*x))) * (1+2*x*prod(k>=0, 1+x^(2^k-1)+2*x^(2^k))). - _Vincenzo Librandi_, Aug 22 2014

%t CoefficientList[Series[(x/((1 - x)^2 (1 + 2 x))) (1 + 2 x Product[1 + x^(2^k-1) + 2 x^(2^k), {k, 0, 20}]), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 22 2014 *)

%Y Cf. A139250, A139251.

%K nonn

%O 0,3

%A _Omar E. Pol_, May 23 2009

%E More terms from _N. J. A. Sloane_, May 17 2010