

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
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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(n1) + a(n4)  a(n5) 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



