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A098246
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Chebyshev polynomials S(n,227) + S(n-1,227) with Diophantine property.
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3
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1, 228, 51755, 11748157, 2666779884, 605347285511, 137411167031113, 31191729568777140, 7080385200945379667, 1607216248885032407269, 364831008111701411070396, 82815031625107335280572623
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| (15*a(n))^2 - 229*b(n)^2 = -4 with b(n)=A098247(n) give all positive solutions of this Pell equation.
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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, 227) + S(n-1, 227) = S(2*n, sqrt(229)), with S(n, x)=U(n, x/2) Chebyshev's polynomials of the second kind, A049310. S(-1, x)= 0 = U(-1, x). S(n, 227)=A098245(n).
a(n)= (-2/15)*I*((-1)^n)*T(2*n+1, 15*I/2) with the imaginary unit I and Chebyshev's polynomials of the first kind. See the T-triangle A053120.
G.f.: (1+x)/(1-227*x+x^2).
a(n)=227*a(n-1)-a(n-2), n>1 ; a(0)=1, a(1)=228 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 18 2008]
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EXAMPLE
| All positive solutions of Pell equation x^2 - 229*y^2 = -4 are
(15=15*1,1), (3420=15*228,226), (776325=15*51755,51301),
(176222355=15*11748157,11645101), ...
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CROSSREFS
| Sequence in context: A103837 A064245 A201238 * A091551 A033528 A086002
Adjacent sequences: A098243 A098244 A098245 * A098247 A098248 A098249
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 10 2004
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