A338329 First differences of A326118.

1, 1, 3, 1, 3, 5, 7, 3, 5, 7, 9, 5, 7, 9, 11, 7, 9, 11, 13, 9, 11, 13, 15, 11, 13, 15, 17, 13, 15, 17, 19, 15, 17, 19, 21, 17, 19, 21, 23, 19, 21, 23, 25, 21, 23, 25, 27, 23, 25, 27, 29, 25, 27, 29, 31, 27, 29, 31, 33, 29, 31, 33, 35, 31, 33, 35, 37, 33, 35, 37, 39

Offset

0,3

Comments

It includes exclusively all the odd numbers (A005408). Except for 1, 3 and 5 that appear three times, each other odd number appears four times.

Links

Table of n, a(n) for n=0..70.

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

Formula

O.g.f.: (1 + 2*x^2 - 2*x^3 + x^4 + 2*x^5 - 2*x^7)/((1 - x)^2*(1 + x + x^2 + x^3)).

E.g.f.: (3*exp(-x) + exp(x)*(7 + 2*x) - 6*cos(x) + 6*sin(x))/4 - 2*x - x^2.

a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7.

a(n) = (7 + 2*n - 6*cos(n*Pi/2) + 3*(-1)^n + 6*sin(n*Pi/2))/4 for n > 2.

Mathematica

LinearRecurrence[{1, 0, 0, 1, -1}, {1, 1, 3, 1, 3, 5, 7, 3}, 71]

Crossrefs

Cf. A004277 (averages of the increasing runs), A005408, A326118.

Sequence in context: A323495 A323554 A323556 * A234587 A339413 A114144

Adjacent sequences: A338326 A338327 A338328 * A338330 A338331 A338332

Keyword

nonn,easy

Author

Stefano Spezia, Oct 23 2020

Status

approved