A257113 a(1) = 2, a(2) = 3; thereafter a(n) is the sum of all the previous terms.

2, 3, 5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120, 10737418240

Offset: 1

Author

Giovanni Teofilatto, Apr 24 2015

Keywords

• nonn
• easy
• less

Comments

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

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

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• E. R. Berlekamp, A contribution to mathematical psychometrics, Unpublished Bell Labs Memorandum, Feb 08 1968 [Annotated scanned copy]
• David Eppstein, Making Change in 2048, arXiv:1804.07396 [cs.DM], 2018.
• Index entries for linear recurrences with constant coefficients, signature (2).

Crossrefs

Cf. A000079, A020714. Essenitally the same as A084215.

Programs

Magma

[2,3] cat [5*2^n: n in [0..35]]; // Vincenzo Librandi, May 15 2015

Mathematica

t = {2, 3}; For[k = 3, k <= 27, k++, AppendTo[t, Total@ t]]; t (* Michael De Vlieger, May 14 2015 *)
Join[{2, 3}, Table[5 2^n, {n, 0, 40}]] (* Vincenzo Librandi, May 15 2015 *)
Join[{2,3},NestList[2#&,5,40]] (* Harvey P. Dale, Apr 06 2018 *)

PARI

a(n) = if(n<3, n+1, 5*2^(n-3)); \\ Altug Alkan, Jul 18 2018

PARI

Vec(x*(1 - x)*(2 + x) / (1 - 2*x) + O(x^40)) \\ Colin Barker, Nov 17 2018

PARI

a(n) = ceil(5*2^(n-3)) \\ Alan Michael Gómez Calderón, Mar 30 2022

Formula

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

a(n) = A146523(n-2) for n>2. - R. J. Mathar, May 14 2015

G.f.: x*(1 - x)*(2 + x) / (1 - 2*x). - Colin Barker, Nov 17 2018