A227380 Doubling the first two of every four nonnegative numbers.

0, 2, 2, 3, 8, 10, 6, 7, 16, 18, 10, 11, 24, 26, 14, 15, 32, 34, 18, 19, 40, 42, 22, 23, 48, 50, 26, 27, 56, 58, 30, 31, 64, 66, 34, 35, 72, 74, 38, 39, 80, 82, 42, 43, 88, 90, 46, 47, 96, 98, 50, 51, 104, 106, 54, 55, 112, 114

Offset: 0

Author

Paul Curtz, Jul 09 2013

Keywords

• nonn
• easy

Comments

a(n) and its differences:

0, 2, 2, 3, 8, 10, 6, 7, 16,...

2, 0, 1, 5, 2, -4, 1, 9, 2,...

-2, 1, 4, -3, -6, 5, 8, -7, -10,... see A103889(n)

3, 3, -7, -3, 11, 3, -15, -3, 19,...

0, -10, 4, 14, -8, -18, 12, 22, -16,...

-10, 14, 10,- 22, -10, 30, 10, -38, -10,... .

The inverse binomial transform is

b(n)=0, 2, -2, 3, 0, -10, 24, -28, 0, 72, -160, 176, 0,...

=(0, 1, -1, 1, 0, -1, 4, -4, 0, 4, -16, 16, 0,...) * a(n).

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-3,4,-3,2,-1).

Crossrefs

Cf. A001477.

Programs

Mathematica

{2#[[1]],2#[[2]],#[[3]],#[[4]]}&/@Partition[Range[0,60],4]//Flatten (* or *) LinearRecurrence[{2,-3,4,-3,2,-1},{0,2,2,3,8,10},60] (* Harvey P. Dale, Dec 14 2021 *)

Formula

a(n) = n*A130658(n+2) = 2*A227316(n)/(n+1).

a(n) - a(n-4) = period 4:repeat 8, 8, 4, 4 = 4*A130658(n+2).

G.f.: (x^5 + 5*x^3 - 2*x^2 + 2*x)/((1-x)^2 * (1+x^2)^2). - Ralf Stephan, Jul 13 2013