A176415 - OEIS

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

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OFFSET

0,1

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

Table of n, a(n) for n=0..104.

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

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

MATHEMATICA

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

PROG

(Magma) &cat[ [7, 1]: n in [0..52] ];

[ 4+3*(-1)^n: n in [0..104] ];

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

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.

Sequence in context: A171544 A344698 A010688 * A356948 A363150 A317846

Adjacent sequences: A176412 A176413 A176414 * A176416 A176417 A176418

KEYWORD

cofr,cons,easy,nonn,mult

AUTHOR

Klaus Brockhaus, Apr 17 2010

STATUS

approved