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A145608
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Numbers a(n)=k such that (1/3)*(5*(2k+1)^2-2) is A057080(n)^2.
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0
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0, 3, 27, 216, 1704, 13419, 105651, 831792, 6548688, 51557715, 405913035, 3195746568, 25160059512, 198084729531, 1559517776739, 12278057484384, 96664942098336, 761041479302307, 5991666892320123, 47172293659258680, 371386682381749320, 2923921165394735883, 23019982640776137747
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..22.
Index entries for linear recurrences with constant coefficients, signature (9,-9,1).
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FORMULA
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a(n+2) = 8*a(n+1) - a(n) + 3.
a(n) = (A070997(n)-1)/2 = 3*A076765(n-1). - R. J. Mathar, Oct 16 2008
a(n) = -1/2 + (1/4)*((4-sqrt(15))^n + (4+sqrt(15))^n) - (1/20)*sqrt(15)*((4-sqrt(15))^n - (4+sqrt(15))^n), with n >= 0. - Paolo P. Lava, Nov 25 2008
G.f.: -3*x / ( (x-1)*(x^2-8*x+1) ). - R. J. Mathar, Nov 27 2011
a(n) = 9*a(n-1) - 9*a(n-2) + a(n-3); a(0)=0, a(1)=3, a(2)=27. - Harvey P. Dale, May 06 2013
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MATHEMATICA
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RecurrenceTable[{a[0]==0, a[1]==3, a[n]==8a[n-1]-a[n-2]+3}, a, {n, 30}] (* or *) LinearRecurrence[{9, -9, 1}, {0, 3, 27}, 30] (* Harvey P. Dale, May 06 2013 *)
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CROSSREFS
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Cf. A057080, A131571, A145607.
Sequence in context: A043023 A198686 A087426 * A083713 A230179 A221769
Adjacent sequences: A145605 A145606 A145607 * A145609 A145610 A145611
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KEYWORD
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easy,nonn
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AUTHOR
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Richard Choulet, Oct 14 2008
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EXTENSIONS
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Made definition and sequence consistent. Changed offset to 0. - R. J. Mathar, Oct 16 2008
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STATUS
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approved
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