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Search: id:A097770
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| A097770 |
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Pell equation solutions (12*b(n))^2 - 145*a(n)^2 = -1 with b(n):=A097769(n), n>=0. |
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+0
4
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| 1, 577, 333505, 192765313, 111418017409, 64399421297089, 37222754091700033, 21514687465581321985, 12435452132351912407297, 7187669817811939790095681, 4154460719243168846762896321, 2401271108052733781489163977857
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Tanya Khovanova, Recursive Sequences
Index entries for sequences related to Chebyshev polynomials.
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FORMULA
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a(n)= S(n, 2*289) - S(n-1, 2*289) = T(2*n+1, sqrt(145))/sqrt(145), 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, 24*I) with the imaginary unit I and Chebyshev polynomials S(n, x) with coefficients shown in A049310.
G.f.: (1-x)/(1-578*x+x^2).
a(n)=578*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=577 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
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(x,y) = (12*1=12;1), (6948=12*579;577), (4015932=12*334661;333505), ... give the positive integer solutions to x^2 - 145*y^2 =-1.
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CROSSREFS
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Cf. A097768 for S(n, 486).
Sequence in context: A163042 A069365 A163053 this_sequence A031522 A158369 A035754
Adjacent sequences: A097767 A097768 A097769 this_sequence A097771 A097772 A097773
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Aug 31 2004
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