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 A065102 a(0) = c, a(1) = p*c^3; a(n+2) = p*c^2*a(n+1) - a(n), for p = 2, c = 3. 1
 3, 54, 969, 17388, 312015, 5598882, 100467861, 1802822616, 32350339227, 580503283470, 10416708763233, 186920254454724, 3354147871421799, 60187741431137658, 1080025197889056045, 19380265820571871152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Integer values of Fibonacci numbers * 3/8 (see 2nd formula). - Vladimir Joseph Stephan Orlovsky, Oct 25 2009 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 (18,-1). FORMULA G.f.: 3/(1 - 18*x + x^2). - Floor van Lamoen, Feb 07 2002 a(n) = 3*A049660(n+1). - R. J. Mathar, Sep 27 2014 MATHEMATICA a[0] = c; a[1] = p*c^3; a[n_] := a[n] = p*c^2*a[n - 1] - a[n - 2]; p = 2; c = 3; Table[ a[n], {n, 0, 20} ] Clear[f, lst, n, a] f[n_]:=Fibonacci[n]; lst={}; Do[a=f[n]*(3/8); If[IntegerQ[a], AppendTo[lst, a]], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2009 *) PROG (PARI): polya002(2, 3, 17). For definition of function polya002 see A052530. (PARI) { p=2; 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("b065102.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 07 2009 CROSSREFS Sequence in context: A119294 A157541 A182159 * A223926 A003776 A222203 Adjacent sequences:  A065099 A065100 A065101 * A065103 A065104 A065105 KEYWORD easy,nonn AUTHOR N. J. A. Sloane, Nov 12 2001 STATUS approved

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Last modified October 19 11:26 EDT 2019. Contains 328216 sequences. (Running on oeis4.)