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A257113
a(1) = 2, a(2) = 3; thereafter a(n) is the sum of all the previous terms.
12
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
1,1
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
E. R. Berlekamp, A contribution to mathematical psychometrics, Unpublished Bell Labs Memorandum, Feb 08 1968 [Annotated scanned copy]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.
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
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 *)
PROG
(Magma) [2, 3] cat [5*2^n: n in [0..35]]; // Vincenzo Librandi, May 15 2015
(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
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Giovanni Teofilatto, Apr 24 2015
STATUS
approved