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%I #24 Jan 01 2023 02:29:09
%S 7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,
%T 7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,
%U 7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7,1,7
%N Periodic sequence: repeat 7,1.
%C Interleaving of A010727 and A000012.
%C Also continued fraction expansion of (7+sqrt(77))/2.
%C Also decimal expansion of 71/99.
%C Essentially first differences of A047521.
%C Binomial transform of A176414.
%C Inverse binomial transform of 2*A020707 preceded by 7.
%C Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 4*x^2 + 4*x^3 + 10*x^4 + 10*x^5 + ... is the o.g.f. for A058187. - _Peter Bala_, Mar 13 2015
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F a(n) = 4+3*(-1)^n.
%F a(n) = a(n-2) for n > 1; a(0) = 7, a(1) = 1.
%F a(n) = -a(n-1)+8 for n > 0; a(0) = 7.
%F a(n) = 7*((n+1) mod 2)+(n mod 2).
%F a(n) = A010688(n+1).
%F G.f.: (7+x)/(1-x^2).
%F Dirichglet g.f.: (1+6*2^(-s))*zeta(s). - _R. J. Mathar_, Apr 06 2011
%F Multiplicative with a(2^e) = 7, and a(p^e) = 1 for p >= 3. - _Amiram Eldar_, Jan 01 2023
%t PadRight[{},120,{7,1}] (* _Harvey P. Dale_, Dec 30 2018 *)
%o (Magma) &cat[ [7, 1]: n in [0..52] ];
%o [ 4+3*(-1)^n: n in [0..104] ];
%o (PARI) a(n)=7-n%2*6 \\ _Charles R Greathouse IV_, Oct 28 2011
%Y Cf. A010727 (all 7's sequence), A000012 (all 1's sequence), A092290 (decimal expansion of (7+sqrt(77))/2), A010688 (repeat 1, 7), A047521 (congruent to 0 or 7 mod 8), A176414 (expansion of (7+8*x)/(1+2*x)), A020707 (2^(n+2)), A058187.
%K cofr,cons,easy,nonn,mult
%O 0,1
%A _Klaus Brockhaus_, Apr 17 2010
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