A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)).

1, 2, 3, 6, 12, 22, 43, 79, 157, 310, 610, 1205, 2381, 4727, 9383, 18699, 37227, 74355, 148660, 296900, 593735, 1187240, 2373810, 4746741, 9491481, 18981027, 37956907, 75910735, 151820416, 303627016, 607253419, 1214497244, 2428978214, 4857918665

Offset: 1

Author

R. K. Guy, May 11 2001

Keywords

• nonn
• easy
• nice

Comments

Arises in analyzing 'put-or-take' games (see Winning Ways, 484-486, 501-503), the prototype being Epstein's Put-or-Take-a-Square game.

References

• E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A060984, A237889.

Programs

Haskell

a060985 n = a060985_list !! (n-1)
a060985_list = iterate a061885 1  -- Reinhard Zumkeller, Feb 03 2012

Mathematica

a[1] = 1; a[n_] := a[n] = Block[ {k = 1}, While[ k*(k + 1)/2 <= a[n - 1], k++ ]; a[n - 1] + k*(k - 1)/2]; Table[ a[n], {n, 1, 40} ]
f[n_]:=Module[{c=Floor[(Sqrt[1+8n]-1)/2]},(c(c+1))/2]; NestList[#+f[#]&, 1, 40] (* Harvey P. Dale, Jun 19 2011 *)

PARI

{ default(realprecision, 1000); for (n=1, 1000, if (n<2, a=1, k=(sqrt(1 + 8*a) - 1)\2; a+=k*(k + 1)/2 ); write("b060985.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 16 2009

Formula

a(n+1) = a(n) + A061883(n) = a(n) + A057944(a(n)) = A061885(a(n)). - Henry Bottomley, May 12 2001

a(n) ~ 0.28276... * 2^n. - Charles R Greathouse IV, Jun 19 2011

Extensions

More terms from David W. Wilson, Henry Bottomley and Robert G. Wilson v, May 12 2001