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A159678
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The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 7*n(j)+1=a(j)*a(j) and 9*n(j)+1=b(j)*b(j) with positive integer numbers.
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4
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1, 17, 271, 4319, 68833, 1097009, 17483311, 278635967, 4440692161, 70772438609, 1127918325583, 17975920770719, 286486814005921, 4565813103324017, 72766522839178351, 1159698552323529599, 18482410314337295233, 294558866477073194129, 4694459453318833810831
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The sequence a(j) is A157456, the sequence n(j) is A159679, the sequence b(j) this sequence here.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (16,-1).
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FORMULA
| The b(j) recurrence (this sequence here) is b(1)=1; b(2)=17; b(t+2)=16*b(t+1)-b(t)
G.f. x*(1+x) / ( 1-16*x+x^2 ). a(n) = A077412(n-1)+A077412(n-2). - R. J. Mathar, Oct 31 2011
a(1)=1, a(2)=17, a(n)=16*a(n-1)-a(n-2) [From Harvey P. Dale, Dec 25 2011]
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MAPLE
| for a from 1 by 2 to 100000 do b:=sqrt((9*a*a-2)/7): if (trunc(b)=b) then
n:=(a*a-1)/7: La:=[op(La), a]:Lb:=[op(Lb), b]:Ln:=[op(Ln), n]: end if: end do:
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MATHEMATICA
| Rest[CoefficientList[Series[x (1+x)/(1-16x+x^2), {x, 0, 30}], x]] (* or *) LinearRecurrence[{16, -1}, {1, 17}, 30] (* From Harvey P. Dale, Dec 25 2011 *)
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PROG
| (Other) sage: [(lucas_number2(n, 16, 1)-lucas_number2(n-1, 16, 1))/14 for n in xrange(1, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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CROSSREFS
| Sequence in context: A135214 A090380 A142898 * A162803 A097830 A163093
Adjacent sequences: A159675 A159676 A159677 * A159679 A159680 A159681
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KEYWORD
| nonn
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AUTHOR
| Paul Weisenhorn (paulweisenhorn(AT)online.de), Apr 19 2009
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EXTENSIONS
| More terms from Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009
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