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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 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 March 31 01:53 EDT 2020. Contains 333133 sequences. (Running on oeis4.)