A176415 Periodic sequence: repeat 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, 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, 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

Offset: 0

Author

Klaus Brockhaus, Apr 17 2010

Keywords

• cofr
• cons
• easy
• nonn
• mult

Comments

Interleaving of A010727 and A000012.

Also continued fraction expansion of (7+sqrt(77))/2.

Also decimal expansion of 71/99.

Essentially first differences of A047521.

Binomial transform of A176414.

Inverse binomial transform of 2*A020707 preceded by 7.

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

Links

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

Crossrefs

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.

Programs

Magma

&cat[ [7, 1]: n in [0..52] ];
[ 4+3*(-1)^n: n in [0..104] ];

Mathematica

PadRight[{},120,{7,1}] (* Harvey P. Dale, Dec 30 2018 *)

PARI

a(n)=7-n%2*6 \\ Charles R Greathouse IV, Oct 28 2011

Formula

a(n) = 4+3*(-1)^n.

a(n) = a(n-2) for n > 1; a(0) = 7, a(1) = 1.

a(n) = -a(n-1)+8 for n > 0; a(0) = 7.

a(n) = 7*((n+1) mod 2)+(n mod 2).

a(n) = A010688(n+1).

G.f.: (7+x)/(1-x^2).

Dirichglet g.f.: (1+6*2^(-s))*zeta(s). - R. J. Mathar, Apr 06 2011

Multiplicative with a(2^e) = 7, and a(p^e) = 1 for p >= 3. - Amiram Eldar, Jan 01 2023