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

Author

Stefano Spezia, Oct 23 2020

Keywords

• nonn
• easy

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

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

Crossrefs

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

Programs

Mathematica

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

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.