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A068073
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Period 4 sequence [ 1, 2, 3, 2, ...].
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7
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1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Continued fraction expansion of (2+sqrt(14))/4. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 01 2010]
The sequence is like a sawtooth wave of period 4. - Michael Somos Feb 13 2011
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,1).
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FORMULA
| G.f.: (1 + 2x + 3x^2 + 2x^3) / (1 - x^4). a(n+4) = a(-n) = a(n).
Conjecture: a(n)=sum{k=0..n, e^(i*pi*(A000120(A001045(n))-A0001045(A000120(n))))}, i=sqrt(-1). - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005
G.f.: (1+x+2x^2)/(1-x+x^2-x^3); a(n)=2-cos(pi*n/2); - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005
a(n)=(1/12)*[7*(n mod 4)+7*((n+1) mod 4)+(n+2) mod 4+(n+3) mod 4] - Paolo P. Lava (paoloplava(AT)gmail.com), Oct 09 2006
Moebius transform is length 4 sequence [ 2, 1, 0, -2]. - Michael Somos Feb 13 2011
a(n) = 2 - A056594(n) - Bruno Berselli, Mar 10 2011.
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EXAMPLE
| 1 + 2*x + 3*x^2 + 2*x^3 + x^4 + 2*x^5 + 3*x^6 + 2*x^7 + x^8 + 2*x^9 + ...
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MATHEMATICA
| CoefficientList[ Series[(1 + 2x + 3x^2 + 2x^3)/(1 - x^4), {x, 0, 85}], x]
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PROG
| (PARI) {a(n) = [ 1, 2, 3, 2] [n%4 + 1]} /* Michael Somos Feb 13 2011 */
(PARI) {a(n) = n%4 + 1 - 2 * (n%4 == 3)} /* Michael Somos Feb 13 2011 */
(PARI) {a(n) = 2 + kronecker( -4, n-1)} /* Michael Somos Feb 13 2011 */
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CROSSREFS
| Cf. A000034, A028356.
Cf. A177033 (decimal expansion of (2+sqrt(14))/4). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 01 2010]
Sequence in context: A124160 A002175 A170823 * A032452 A084199 A030314
Adjacent sequences: A068070 A068071 A068072 * A068074 A068075 A068076
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KEYWORD
| easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 01 2002
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