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A065100
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a(0) = c, a(1) = p*c^3; a(n+2) = p*c^2*a(n+1) - a(n), for p = 1, c = 3.
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8
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3, 27, 240, 2133, 18957, 168480, 1497363, 13307787, 118272720, 1051146693, 9342047517, 83027280960, 737903481123, 6558104049147, 58285032961200, 518007192601653, 4603779700453677, 40916010111481440, 363640311302879283
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,100
Index entries for sequences related to linear recurrences with constant coefficients
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.
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FORMULA
| G.f.: 3/(1-9*x+x^2).
a(n)= 3*A018913(n+1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2009]
a(n)=9*a(n-1)-a(n-2) (with a(0)=3, a(1)=27) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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EXAMPLE
| a(2)=9*27-3=240; a(3)=9*240-27=2133; a(4)=9*2133-240=18957 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 07 2010]
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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} ]
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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 (hjsmithh(AT)sbcglobal.net), Oct 07 2009]
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CROSSREFS
| Cf. A052530.
Sequence in context: A087426 A145608 A083713 * A035088 A013708 A102518
Adjacent sequences: A065097 A065098 A065099 * A065101 A065102 A065103
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KEYWORD
| easy,nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 12 2001
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EXTENSIONS
| More terms from Marc LeBrun (mlb(AT)well.com) and Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 12 2001
Gen. func. from Floor van Lamoen (fvlamoen(AT)hotmail.com), Feb 07 2002
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