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A145608 Numbers a(n)=k such that (1/3)*(5*(2k+1)^2-2) is A057080(n)^2. 0
0, 3, 27, 216, 1704, 13419, 105651, 831792, 6548688, 51557715, 405913035, 3195746568, 25160059512, 198084729531, 1559517776739, 12278057484384, 96664942098336, 761041479302307, 5991666892320123, 47172293659258680, 371386682381749320, 2923921165394735883, 23019982640776137747 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (9,-9,1).

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A057080, A131571, A145607.

Sequence in context: A043023 A198686 A087426 * A083713 A230179 A221769

Adjacent sequences:  A145605 A145606 A145607 * A145609 A145610 A145611

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 14 2008

EXTENSIONS

Made definition and sequence consistent. Changed offset to 0. - R. J. Mathar, Oct 16 2008

STATUS

approved

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Last modified August 7 10:19 EDT 2022. Contains 355985 sequences. (Running on oeis4.)