A147818 Period 4: repeat [5, 9, 9, 5].

5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5, 9, 9, 5, 5

Offset: 1

Author

Omar E. Pol, Nov 14 2008, Jan 25 2009

Keywords

• base
• easy
• nonn

Comments

Last digit of the number whose binary representation is the concatenation of n 1's, 2n-1 0's and n 1's.

a(n) is the final digit of A147539(n).

Links

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

Crossrefs

Cf. A138120, A147539.

Programs

Magma

&cat [[5, 9, 9, 5]^^30]; // Wesley Ivan Hurt, Jul 09 2016

Maple

A010879 := proc(n) n mod 10; end:
A147539 := proc(n) 2^n-1+2^(4*n-1)-2^(3*n-1); end:
A147818 := proc(n) A010879(A147539(n)); end: # R. J. Mathar, Jan 22 2009
seq(op([5, 9, 9, 5]), n=1..40); # Wesley Ivan Hurt, Jul 09 2016

Mathematica

PadRight[{}, 100, {5, 9, 9, 5}] (* Wesley Ivan Hurt, Jul 09 2016 *)

Formula

a(n+1) = 7-2*cos(Pi*n/2)+2*sin(Pi*n/2). - R. J. Mathar, Oct 08 2011

a(n) = a(n-1)-a(n-2)+a(n-3) for n>3. G.f.: x*(5*x^2+4*x+5)/((1-x)*(x^2+1)). [Colin Barker, Nov 04 2012]

a(n) = a(n-4) for n>4. - Wesley Ivan Hurt, Jul 09 2016

Extensions

More terms from R. J. Mathar, Jan 22 2009