A197916 Related to the periodic sequence A171654.

0, 1, 6, 7, 2, 3, 8, 9, 4, 5, 10, 11, 6, 7, 12, 13, 8, 9, 14, 15, 10, 11, 16, 17, 12, 13, 18, 19, 14, 15, 20, 21, 16, 17, 22, 23, 18, 19, 24, 25, 20, 21, 26, 27, 22, 23, 28, 29, 24, 25, 30, 31, 26, 27, 32, 33, 28, 29, 34, 35, 30, 31, 36, 37, 32, 33, 38, 39

Offset: 0

Author

Philippe Deléham, Oct 19 2011

Keywords

• easy
• nonn

Comments

All numbers appear twice except numbers 0,1,2,3,4,5 which appear once. - From A. Salagnad, Oct 19 2011.

Links

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

Crossrefs

Cf. A171654.

Programs

Mathematica

LinearRecurrence[{1,0,0,1,-1},{0,1,6,7,2},80] (* Harvey P. Dale, Jul 30 2019 *)

PARI

a(n)=([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; -1,1,0,0,1]^n*[0;1;6;7;2])[1,1] \\ Charles R Greathouse IV, Jul 06 2017

Formula

a(n)=A171654(n) mod 10.

a(n)=Sum_k>=0 {A030308(n,k)*b(k)} with b(0)=1, b(1)=6 and b(k)=2^(k-1) for k>1.

G.f. ( -x*(-1-5*x-x^2+5*x^3) ) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 20 2011

a(n) = n/2+(11-(-1)^n)/4 -5*A057077(n)/2. - R. J. Mathar, Oct 20 2011