A131369 Period 10: repeat [5, 4, 5, 4, 3, 4, 5, 4, 5, 0].

5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3, 4, 5, 4, 5, 0, 5, 4, 5, 4, 3

Offset

0,1

Comments

Differences: [-1, 1, -1, -1, 1, 1, -1, 1, -5, 5].

Links

Table of n, a(n) for n=0..104.

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

Formula

From Wesley Ivan Hurt, Aug 29 2015: (Start)

G.f.: (5+4*x+5*x^2+4*x^3+3*x^4+4*x^5+5*x^6+4*x^7+5*x^8)/(1-x^10).

a(n) = a(n-10), n>9.

a(n) = (9+(-1)^n)/2+((-1)^n-3)*(floor((n+1)/5)-floor(n/5)). (End)

Maple

A131369:=n->[5, 4, 5, 4, 3, 4, 5, 4, 5, 0][(n mod 10)+1]: seq(A131369(n), n=0..100); # Wesley Ivan Hurt, Aug 29 2015

Mathematica

CoefficientList[Series[(5 + 4 x + 5 x^2 + 4 x^3 + 3 x^4 + 4 x^5 + 5 x^6 + 4 x^7 + 5 x^8)/(1 - x^10), {x, 0, 100}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {5, 4, 5, 4, 3, 4, 5, 4, 5, 0}, 100] (* Wesley Ivan Hurt, Aug 29 2015 *)

Prog

(Magma) I:=[5, 4, 5, 4, 3, 4, 5, 4, 5, 0]; [n le 10 select I[n] else Self(n-10): n in [1..100]]; // Wesley Ivan Hurt, Aug 29 2015

Crossrefs

Sequence in context: A361803 A344124 A237577 * A122219 A093348 A262604

Adjacent sequences: A131366 A131367 A131368 * A131370 A131371 A131372

Keyword

nonn,easy

Author

Paul Curtz, Sep 30 2007

Status

approved