A296070 Partial sums of A296069.

0, 2, 3, 8, 5, 12, 7, 16, 9, 20, 11, 24, 13, 28, 15, 32, 17, 36, 19, 40, 21, 44, 23, 48, 25, 52, 27, 56, 29, 60, 31, 64, 33, 68, 35, 72, 37, 76, 39, 80, 41, 84, 43, 88, 45, 92, 47, 96, 49, 100, 51, 104, 53, 108, 55, 112, 57, 116, 59, 120

Offset: 1

Author

Enrique Navarrete, Dec 04 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A296069.

Programs

Mathematica

Accumulate@ 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}, 59] (* Michael De Vlieger, Dec 12 2017 *)

PARI

concat(0, Vec(x^2*(2 + 3*x + 4*x^2 - x^3 - 2*x^4) / ((1 - x)^2*(1 + x)^2) + O(x^80))) \\ Colin Barker, Mar 19 2020

Formula

From Colin Barker, Mar 19 2020: (Start)

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

a(n) = 2*a(n-2) - a(n-4) for n>6.

a(n) = (3 + (-1)^n)*n / 2 for n>2.

(End)