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Search: id:A060985
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A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)). +0
5
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 (list; graph; listen)
OFFSET

1,2

COMMENT

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

FORMULA

a(n+1) = a(n)+A061883(n) = a(n)+A057944(a(n)) = A061885(a(n)) - Henry Bottomley (se16(AT)btinternet.com), May 12 2001

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} ]

PROGRAM

(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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 16 2009]

CROSSREFS

Cf. A060984.

Sequence in context: A018178 A112575 A018079 this_sequence A068012 A019138 A154324

Adjacent sequences: A060982 A060983 A060984 this_sequence A060986 A060987 A060988

KEYWORD

nonn,easy,nice

AUTHOR

R. K. Guy (rkg(AT)cpsc.ucalgary.ca), May 11 2001

EXTENSIONS

More terms from David W. Wilson (davidwwilson(AT)comcast.net), Henry Bottomley and Robert G. Wilson v, May 12, 2001

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Last modified December 10 00:48 EST 2009. Contains 170565 sequences.


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