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A097738
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Pell equation solutions (9*a(n))^2 - 82*b(n)^2 = -1 with b(n):=A097739(n), n>=0.
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2
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1, 327, 106601, 34751599, 11328914673, 3693191431799, 1203969077851801, 392490226188255327, 127950609768293384801, 41711506294237455189799, 13597823101311642098489673, 4432848619521301086652443599
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
| a(n)= S(n, 2*163) + S(n-1, 2*163) = S(2*n, 2*sqrt(82)), with Chebyshev polynomials of the 2nd kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x).
a(n)= ((-1)^n)*T(2*n+1, 9*I)/(9*I) with the imaginary unit I and Chebyshev polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-2*163*x+x^2).
a(n)=326*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=327 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| (x,y) = (9*1=9;1), (2943=9*327;325), (959409=9*106601;105949), ... give the positive integer solutions to x^2 - 82*y^2 =-1.
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CROSSREFS
| Cf. A097737 for S(n, 2*163).
Sequence in context: A203723 A097737 A126311 * A183848 A205251 A138078
Adjacent sequences: A097735 A097736 A097737 * A097739 A097740 A097741
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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