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A338329 First differences of A326118. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 14 18:27 EDT 2021. Contains 345038 sequences. (Running on oeis4.)