A081695 - OEIS

A081695

From P-positions in a certain game. Pile 2 tokens for select function (1+(-)^(y1+1))x1/2.

0, 1, 3, 7, 12, 13, 21, 30, 31, 42, 45, 60, 61, 78, 79, 98, 99, 121, 144, 145, 170, 171, 198, 199, 228, 231, 264, 265, 300, 301, 338, 339, 378, 379, 420, 422, 423, 469, 516, 517, 566, 567, 618, 619, 672, 673, 728, 729, 786, 787, 846, 849, 912, 913, 978, 979, 1046, 1047, 1116, 1117, 1188, 1189, 1262, 1263, 1338

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..64.

A. S. Fraenkel, New games related to old and new sequences, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 4, Paper G6, 2004.

FORMULA

Let a(n) = A081694(n) and let b(n) = n-th term of the current sequence. Then a(n) = mex{ a(i), b(i) : 0 <= i < n}; b(n) = a(n) + b(n-1) - (1+(-1)^b(n-1))*a(n-1)/2. Also, apart from initial zero, current sequence is complement of A081694.

MAPLE

A081694 := proc(n)

option remember;

local i;

if n <=1 then

else

{ seq(procname(i), i=0..n-1)} union {seq(A081695(i), i=0..n-1)} ;

mex(%) ;

end if;

end proc:

A081695 := proc(n)

option remember;

if n <= 1 then

else

A081694(n)+procname(n-1)-(1+(-1)^procname(n-1))*A081694(n-1)/2 ;

end if;

end proc:

seq(A081695(n), n=0..70) ; # R. J. Mathar, Apr 13 2019

CROSSREFS

Cf. A081694.

Sequence in context: A230109 A045134 A215631 * A290955 A270122 A142958

Adjacent sequences: A081692 A081693 A081694 * A081696 A081697 A081698

KEYWORD

nonn,easy,changed

AUTHOR

N. J. A. Sloane, Apr 02 2003

EXTENSIONS

More terms from R. J. Mathar, Apr 13 2019

STATUS

approved