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URL: https://oeis.org/A197916

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A197916
Related to the periodic sequence A171654.
0
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
0,3
COMMENTS
All numbers appear twice except numbers 0,1,2,3,4,5 which appear once. - A. Salagnad, Oct 19 2011
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.
From R. J. Mathar, Oct 20 2011: (Start)
G.f.: -x*(-1-5*x-x^2+5*x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ).
a(n) = n/2 + (11-(-1)^n)/4 - 5*A057077(n)/2. (End)
MATHEMATICA
LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 6, 7, 2}, 80] (* Harvey P. Dale, Jul 30 2019 *)
PROG
(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
CROSSREFS
Cf. A171654.
Sequence in context: A198098 A021941 A171654 * A216103 A198823 A353053
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Oct 19 2011
STATUS
approved