A145608 Numbers a(n)=k such that (1/3)*(5*(2k+1)^2-2) is A057080(n)^2.

0, 3, 27, 216, 1704, 13419, 105651, 831792, 6548688, 51557715, 405913035, 3195746568, 25160059512, 198084729531, 1559517776739, 12278057484384, 96664942098336, 761041479302307, 5991666892320123, 47172293659258680, 371386682381749320, 2923921165394735883, 23019982640776137747

Offset: 0

Author

Richard Choulet, Oct 14 2008

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A057080, A131571, A145607.

Programs

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 *)

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

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

Extensions

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