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A065100 a(0) = c, a(1) = p*c^3; a(n+2) = p*c^2*a(n+1) - a(n), for p = 1, c = 3. 8
3, 27, 240, 2133, 18957, 168480, 1497363, 13307787, 118272720, 1051146693, 9342047517, 83027280960, 737903481123, 6558104049147, 58285032961200, 518007192601653, 4603779700453677, 40916010111481440, 363640311302879283 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..100

Tanya Khovanova, Recursive Sequences

J.-P. Ehrmann et al., Problem POLYA002, Integer pairs (x,y) for which (x^2+y^2)/(1+pxy) is an integer.

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

FORMULA

G.f.: 3/(1 - 9*x + x^2). - Floor van Lamoen, Feb 07 2002

a(n) = 3*A018913(n+1). - R. J. Mathar, Oct 26 2009

a(n) = 9*a(n-1) - a(n-2) (with a(0)=3, a(1)=27). - Vincenzo Librandi, Aug 07 2010

EXAMPLE

From Vincenzo Librandi, Aug 07 2010: (Start)

a(2) = 9*27 - 3 = 240;

a(3) = 9*240 - 27 = 2133;

a(4) = 9*2133 - 240 = 18957. (End)

MATHEMATICA

a[0] = c; a[1] = p*c^3; a[n_] := a[n] = p*c^2*a[n - 1] - a[n - 2]; p = 1; c = 3; Table[ a[n], {n, 0, 20} ]

LinearRecurrence[{9, -1}, {3, 27}, 30] (* Harvey P. Dale, Sep 22 2016 *)

PROG

(PARI): polya002(1, 3, 20). For definition of function polya002 see A052530.

(PARI) { p=1; c=3; k=p*c^2; for (n=0, 100, if (n>1, a=k*a1 - a2; a2=a1; a1=a, if (n, a=a1=k*c, a=a2=c)); write("b065100.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 07 2009

CROSSREFS

Cf. A052530.

Sequence in context: A083713 A230179 A221769 * A035088 A268094 A013708

Adjacent sequences:  A065097 A065098 A065099 * A065101 A065102 A065103

KEYWORD

easy,nonn

AUTHOR

N. J. A. Sloane, Nov 12 2001

STATUS

approved

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Last modified July 22 19:35 EDT 2018. Contains 312918 sequences. (Running on oeis4.)