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Search: id:A081555
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| A081555 |
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a(n)=6a(n-1)-a(n-2)-4, a(0)=3, a(1)=7. |
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+0
2
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| 3, 7, 35, 199, 1155, 6727, 39203, 228487, 1331715, 7761799, 45239075, 263672647, 1536796803, 8957108167, 52205852195, 304278004999, 1773462177795, 10336495061767, 60245508192803, 351136554095047, 2046573816377475
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n)=A003499(n)+1. a(2n)+1=A003499(n)^2. 2(a(2n+1)+1) is a perfect square.
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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) = (3+2sqrt(2))^n + (3-2sqrt(2))^n + 1
G.f.: (3-14x+7x^2)/((1-x)(1-6x+x^2))
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MATHEMATICA
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r[n_] := r[n] = 6*r[n - 1] - r[n - 2] - 4; r[0] = 3; r[1] = 7; Table[r[n], {n, 0, 25}]
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PROGRAM
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(PARI) a(n)=1+2*real((3+quadgen(32))^n)
(PARI) a(n)=1+2*subst(poltchebi(abs(n)), x, 3)
(PARI) a(n)=if(n<0, a(-n), 1+polsym(1-6*x+x^2, n)[n+1])
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CROSSREFS
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a(n)=A051927(2n).
Sequence in context: A006099 A053530 A132102 this_sequence A027624 A063042 A108505
Adjacent sequences: A081552 A081553 A081554 this_sequence A081556 A081557 A081558
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Mar 24 2003
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