A296064 -id:A296064 - cp's OEIS frontend

A296065 Partial sums of A296064.

0, 2, 3, 0, 5, 0, 7, 0, 9, 0, 11, 0, 13, 0, 15, 0, 17, 0, 19, 0, 21, 0, 23, 0, 25, 0, 27, 0, 29, 0, 31, 0, 33, 0, 35, 0, 37, 0, 39, 0, 41, 0, 43, 0, 45, 0, 47, 0, 49, 0, 51, 0, 53, 0, 55

Offset: 1

Enrique Navarrete, Dec 04 2017

Essentially the same as A193356. - R. J. Mathar, Jan 02 2018

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A296064.

Accumulate@ Nest[Append[#, Block[{k = 1, s = 1}, While[Nand[FreeQ[#, s k], IntegerQ@ Mean[Append[#, s k]]], If[s == 1, s = -1, k++; s = 1]]; s k]] &, {0}, 54] (* Michael De Vlieger, Dec 12 2017 *)
LinearRecurrence[{0,2,0,-1},{0,2,3,0,5,0},60] (* or *) Join[{0,2},Riffle[ 2*Range[ 30]+1,0]]  (* Harvey P. Dale, Oct 21 2021 *)

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).

Original entry on oeis.org

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

Enrique Navarrete, Dec 04 2017

sign

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-1,1,1).

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

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 *)

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

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)

cp's OEIS Frontend

A296065 Partial sums of A296064.

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