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A097730
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Pell equation solutions (6*b(n))^2 - 37*a(n)^2 = -1 with b(n):=A097729(n), n>=0.
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4
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1, 145, 21169, 3090529, 451196065, 65871534961, 9616792908241, 1403985893068225, 204972323595052609, 29924555258984612689, 4368780095488158399985, 637811969386012141785121
(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*73) - S(n-1, 2*73) = T(2*n+1, sqrt(37)/sqrt(37), 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, 12*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-146*x+x^2).
a(n)=146*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=145 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| (x,y) = (6,1), (882,145), (128766,21169), ... give the positive integer solutions to x^2 - 37*y^2 =-1.
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CROSSREFS
| Cf. A097729 for S(n, 146).
Row 6 of array A188647.
Sequence in context: A192842 A012813 A018232 * A060720 A015081 A015055
Adjacent sequences: A097727 A097728 A097729 * A097731 A097732 A097733
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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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