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A131027
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Periodic sequence (4, 3, 1, 0, 1, 3).
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10
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4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1, 0, 1, 3, 4, 3, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Third column of triangular array T defined in A131022.
a(n) = abs(A078070(n+1)).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,-2,1).
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FORMULA
| a(1) = 4, a(2) = a(6) = 3, a(3) = a(5) = 1, a(4) = 0, a(6) = 1; for n > 6, a(n) = a(n-6).
G.f.: (4-5*x+3*x^2)/((1-x)*(1-x+x^2)).
a(n)=1/30*{-(n mod 6)-6*[(n+1) mod 6]-[(n+2) mod 6]+9*[(n+3) mod 6]+14*[(n+4) mod 6]+9*[(n+5) mod 6]}, with n>=0. - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 19 2007
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PROG
| (PARI) {m=105; for(n=1, m, r=(n-1)%6; print1(if(r==0, 4, if(r==1||r==5, 3, if(r==3, 0, 1))), ", "))}
(MAGMA) m:=105; [ [4, 3, 1, 0, 1, 3][(n-1) mod 6 + 1]: n in [1..m] ];
(Other) sage: [(lucas_number2(n, 2, 1)-lucas_number2(n-1, 1, 1)) for n in xrange(4, 109)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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CROSSREFS
| Cf. A131022, A078070. Other columns of T are in A088911, A131026, A131028, A131029, A131030.
Sequence in context: A010102 A144161 A054669 * A133475 A021236 A136590
Adjacent sequences: A131024 A131025 A131026 * A131028 A131029 A131030
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KEYWORD
| nonn,easy
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AUTHOR
| Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), following a suggestion of Paul Curtz (bpcrtz(AT)free.fr), Jun 10 2007
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