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A097773
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Pell equation solutions (13*b(n))^2 - 170*a(n)^2 = -1 with b(n):=A097772(n), n>=0.
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3
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1, 677, 459005, 311204713, 210996336409, 143055204880589, 96991217912702933, 65759902689607707985, 44585117032336113310897, 30228643588021195217080181, 20494975767561338021067051821
(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)= ((-1)^n)*S(2*n, 26*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-678*x+x^2).
a(n)= S(n, 2*339) - S(n-1, 2*339) = T(2*n+1, sqrt(170))/sqrt(170), 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)=678*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=677 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| (x,y) = (13*1=13;1), (8827=13*679;677), (5984693=13*460361;459005), ... give the positive integer solutions to x^2 - 170*y^2 =-1.
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CROSSREFS
| Cf. A097771 for S(n, 678).
Row 13 of array A188647.
Sequence in context: A108824 A205471 A144381 * A031524 A158385 A186127
Adjacent sequences: A097770 A097771 A097772 * A097774 A097775 A097776
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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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