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A097739
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Pell equation solutions (9*b(n))^2 - 82*a(n)^2 = -1 with b(n):=A097738(n), n>=0.
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4
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1, 325, 105949, 34539049, 11259624025, 3670602893101, 1196605283526901, 390089651826876625, 127168029890278252849, 41456387654578883552149, 13514655207362825759747725, 4405736141212626618794206201
(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) = T(2*n+1, sqrt(82))/sqrt(82), with Chebyshev polynomials of the 2nd and first kind. See A049310 for the triangle of S(n, x)= U(n, x/2) coefficients. S(-1, x) := 0 =: U(-1, x); and A053120 for the T-triangle.
a(n)= ((-1)^n)*S(2*n, 18*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1- 326*x+x^2).
a(n)=326*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=325 . [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, 326).
Row 9 of array A188647.
Sequence in context: A166220 A121000 A048909 * A203188 A048918 A031516
Adjacent sequences: A097736 A097737 A097738 * A097740 A097741 A097742
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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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