A131715 -id:A131715

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A156551

Period 10: repeat [8,6,0,4,2,2,4,0,6,8].

+10
1

8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8, 8, 6, 0, 4, 2, 2, 4, 0, 6, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

See A131715.

LINKS

Table of n, a(n) for n=0..89.

FORMULA

a(n) = A155110(n) mod 10.

G.f.: 2*(4*x^8-x^7+x^6+x^5+x^3+x^2-x+4)/((1-x)*(x^4-x^3+x^2-x+1)*(x^4+x^3+x^2+x+1)). - R. J. Mathar, Feb 23 2009

a(n) = (15*(4-m^4+8*m^3-19*m^2+12*m)-2*(m^3-6*m^2+17*m-18)*(-1)^floor(n/5))/12 where m = n-5*floor(n/5). - Luce ETIENNE, Oct 13 2017

CROSSREFS

Cf. A010874, A131715, A155110.

KEYWORD

nonn,easy,less

AUTHOR

Paul Curtz, Feb 09 2009

EXTENSIONS

Edited by R. J. Mathar, Feb 23 2009

More terms from Jinyuan Wang, Feb 26 2020

STATUS

approved

A131036

First differences of A131711.

+10
0

1, 1, 3, -3, 7, -9, 9, -1, -3, 3, -7, -1, 1, 1, 3, -3, 7, -9, 9, -1, -3, 3, -7, -1, 1, 1, 3, -3, 7, -9, 9, -1, -3, 3, -7, -1, 1, 1, 3, -3, 7, -9, 9, -1, -3, 3, -7, -1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

The equivalent operation on A001333 yields last digits A131707 and their first differences A131715.

LINKS

Table of n, a(n) for n=0..47.

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

FORMULA

a(n) = a(n-12).

From Chai Wah Wu, Jan 09 2021: (Start)

a(n) = - a(n-1) - a(n-4) - a(n-5) - a(n-8) - a(n-9) for n > 8.

G.f.: (x^8 + 8*x^7 + 4*x^6 + 5*x^4 + 4*x^2 + 2*x + 1)/(x^9 + x^8 + x^5 + x^4 + x + 1). (End)

MATHEMATICA

Differences[PadRight[{}, 120, {0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1}]] (* Harvey P. Dale, Dec 29 2014 *)

CROSSREFS

Cf. A131711.

KEYWORD

sign

AUTHOR

Paul Curtz, Sep 23 2007

EXTENSIONS

Edited by R. J. Mathar, Jul 07 2008

STATUS

approved

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