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Search: id:A054318
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| 1, 5, 45, 441, 4361, 43165, 427285, 4229681, 41869521, 414465525, 4102785725, 40613391721, 402031131481, 3979697923085, 39394948099365, 389969783070561, 3860302882606241, 38213059042991845, 378270287547312205
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OFFSET
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1,2
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COMMENT
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A two-way infinite sequence which is palindromic.
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LINKS
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Index entries for two-way infinite sequences
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FORMULA
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a(n) = 11(a(n-1) - a(n-2)) + a(n-3); a(n)=1/2 + (3 - sqrt(6))/12*(5 + 2sqrt(6))^n + (3 + sqrt(6))/12*(5 - 2sqrt(6))^n
G.f.: x(1-6x+x^2)/((1-x)(1-10x+x^2)). 12a(n)a(n-1)+4=(a(n)+a(n-1)+2)^2. a(n)=a(1-n)=10a(n-1)-a(n-2)-4=12a(n-1)^2/(a(n-1)+a(n-2))-a(n-1)=(a(n-1)+4)a(n-1)/a(n-2). - Michael Somos, Mar 18, 2003
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EXAMPLE
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a(2)=5 because the 5th Star number (A003154) 121=11^2 is the 2nd that is a square
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PROGRAM
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(PARI) a(n)=if(n<1, a(1-n), 1/2+subst(poltchebi(n)+poltchebi(n-1), x, 5)/12)
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CROSSREFS
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A031138 is 3*a(n)-2. Cf. A003154.
Sequence in context: A005979 A165225 A121272 this_sequence A093140 A137233 A001449
Adjacent sequences: A054315 A054316 A054317 this_sequence A054319 A054320 A054321
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KEYWORD
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easy,nonn
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AUTHOR
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Ignacio Larrosa Canestro (ignacio.larrosa(AT)eresmas.net) Feb 27 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Mar 01 2000
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