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A176040 Periodic sequence: Repeat 3, 1. 4
3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Interleaving of A010701 and A000012.

Also continued fraction expansion of (3+sqrt(21))/2.

Also decimal expansion of 31/99.

a(n) = A010684(n+1).

Essentially first differences of A014601.

Inverse binomial transform of 3 followed by A020707.

Second inverse binomial transform of A052919 without initial term 2.

Third inverse binomial transform of A007582 without initial term 1.

Exp( Sum_{n >= 1} a(n)*x^n/n ) = 1 + x + 2*x^2 + 2*x^3 + 3*x^4 + 3*x^5 + ... is the o.g.f. for A008619. - 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) = 2+(-1)^n.

a(n) = a(n-2) for n > 1; a(0) = 3, a(1) = 1.

a(n) = -a(n-1)+4 for n > 0; a(0) = 3.

a(n) = 3*((n+1) mod 2)+(n mod 2).

G.f.: (3+x)/((1-x)*(1+x)).

MATHEMATICA

PadRight[{}, 120, {3, 1}] (* or *) LinearRecurrence[{0, 1}, {3, 1}, 120] (* Harvey P. Dale, Mar 11 2015 *)

PROG

(MAGMA) &cat[ [3, 1]: n in [0..52] ];

[ 2+(-1)^n: n in [0..104] ];

CROSSREFS

Cf. A010701 (all 3's sequence), A000012 (all 1's sequence), A090458 (decimal expansion of (3+sqrt(21))/2), A010684 (repeat 1, 3), A014601 (congruent to 0 or 3 mod 4), A020707 (2^(n+2)), A052919, A007582 (2^(n-1)*(1+2^n)), A008619.

Sequence in context: A153284 A112030 A010684 * A125768 A266875 A307193

Adjacent sequences:  A176037 A176038 A176039 * A176041 A176042 A176043

KEYWORD

cofr,cons,easy,nonn,mult

AUTHOR

Klaus Brockhaus, Apr 07 2010

STATUS

approved

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Last modified October 15 10:46 EDT 2019. Contains 328026 sequences. (Running on oeis4.)