A296069 a(1)=0; thereafter a(n) is the smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), ..., a(n) is a nonzero integer. Preference is given to positive values of a(n).

0, 2, 1, 5, -3, 7, -5, 9, -7, 11, -9, 13, -11, 15, -13, 17, -15, 19, -17, 21, -19, 23, -21, 25, -23, 27, -25, 29, -27, 31, -29, 33, -31, 35, -33, 37, -35, 39, -37, 41, -39, 43, -41, 45, -43, 47, -45, 49, -47, 51, -49, 53, -51

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (-1,1,1).

Formula

From Colin Barker, Mar 14 2020: (Start)

G.f.: x^2*(2 + 3*x + 4*x^2 - x^3 - 2*x^4) / ((1 - x)*(1 + x)^2).

a(n) = -a(n-1) + a(n-2) + a(n-3) for n>6.

(End)

Mathematica

Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], And[IntegerQ@ Mean@ #, Total@ # != 0] &@ Append[#, s k]], If[s == 1, s = -1, k++; s = 1]]; s k]] &, {0}, 52] (* Michael De Vlieger, Dec 12 2017 *)

Prog

(PARI) concat(0, Vec(x^2*(2 + 3*x + 4*x^2 - x^3 - 2*x^4) / ((1 - x)*(1 + x)^2) + O(x^65))) \\ Colin Barker, Mar 14 2020

Crossrefs

Cf. A296063, A296064, A296070 (partial sums).

Sequence in context: A182650 A127367 A054084 * A058683 A286295 A026205

Adjacent sequences: A296066 A296067 A296068 * A296070 A296071 A296072

Keyword

sign

Author

Enrique Navarrete, Dec 04 2017

Status

approved