%I #59 Jul 18 2023 09:22:24

%S 2,3,5,10,20,40,80,160,320,640,1280,2560,5120,10240,20480,40960,81920,

%T 163840,327680,655360,1310720,2621440,5242880,10485760,20971520,

%U 41943040,83886080,167772160,335544320,671088640,1342177280,2684354560,5368709120,10737418240

%N a(1) = 2, a(2) = 3; thereafter a(n) is the sum of all the previous terms.

%C Except for first three terms, a(n) is 10 times 2^(n-4).

%C These values comprise the tile values used in the "fives" variant of the game 2048, including 1 as the zeroth term. - _Michael De Vlieger_, Jul 18 2018

%H Colin Barker, <a href="/A257113/b257113.txt">Table of n, a(n) for n = 1..1000</a>

%H E. R. Berlekamp, <a href="/A257113/a257113.pdf">A contribution to mathematical psychometrics</a>, Unpublished Bell Labs Memorandum, Feb 08 1968 [Annotated scanned copy]

%H David Eppstein, <a href="https://arxiv.org/abs/1804.07396">Making Change in 2048</a>, arXiv:1804.07396 [cs.DM], 2018.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).

%F a(n) = A020714(n-3) for n>2.

%F a(n) = A146523(n-2) for n>2. - _R. J. Mathar_, May 14 2015

%F G.f.: x*(1 - x)*(2 + x) / (1 - 2*x). - _Colin Barker_, Nov 17 2018

%t t = {2, 3}; For[k = 3, k <= 27, k++, AppendTo[t, Total@ t]]; t (* _Michael De Vlieger_, May 14 2015 *)

%t Join[{2, 3}, Table[5 2^n, {n, 0, 40}]] (* _Vincenzo Librandi_, May 15 2015 *)

%t Join[{2,3},NestList[2#&,5,40]] (* _Harvey P. Dale_, Apr 06 2018 *)

%o (Magma) [2,3] cat [5*2^n: n in [0..35]]; // _Vincenzo Librandi_, May 15 2015

%o (PARI) a(n) = if(n<3, n+1, 5*2^(n-3)); \\ _Altug Alkan_, Jul 18 2018

%o (PARI) Vec(x*(1 - x)*(2 + x) / (1 - 2*x) + O(x^40)) \\ _Colin Barker_, Nov 17 2018

%o (PARI) a(n) = ceil(5*2^(n-3)) \\ _Alan Michael Gómez Calderón_, Mar 30 2022

%Y Cf. A000079, A020714, A084215.

%K nonn,easy,less

%O 1,1

%A _Giovanni Teofilatto_, Apr 24 2015