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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). a(n)= 3*A018913(n+1). [From R. J. Mathar, Oct 26 2009] a(n)=9*a(n-1)-a(n-2) (with a(0)=3, a(1)=27) [From Vincenzo Librandi, Aug 07 2010] EXAMPLE a(2)=9*27-3=240; a(3)=9*240-27=2133; a(4)=9*2133-240=18957 [From Vincenzo Librandi, Aug 07 2010] 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) ) } [From 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 EXTENSIONS Gen. func. from Floor van Lamoen, Feb 07 2002 STATUS approved

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