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

0,2

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

Table of n, a(n) for n=0..57.

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

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

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 *)

Crossrefs

Cf. A001477.

Sequence in context: A300354 A091681 A076541 * A159789 A153932 A158763

Adjacent sequences: A227377 A227378 A227379 * A227381 A227382 A227383

Keyword

nonn

Author

Paul Curtz, Jul 09 2013

Status

approved