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Search: id:A065102
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| A065102 |
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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 = 2, c = 3. |
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1
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| 3, 54, 969, 17388, 312015, 5598882, 100467861, 1802822616, 32350339227, 580503283470, 10416708763233, 186920254454724, 3354147871421799, 60187741431137658, 1080025197889056045, 19380265820571871152
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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A065102 == Integer numbers of Fibonacci Number * (3/8). [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2009]
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LINKS
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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
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G.f.: 3/(1-18*x+x^2).
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MATHEMATICA
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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 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2009]
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PROGRAM
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(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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 07 2009]
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CROSSREFS
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Sequence in context: A045481 A119294 A157541 this_sequence A003776 A157550 A091826
Adjacent sequences: A065099 A065100 A065101 this_sequence A065103 A065104 A065105
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 12 2001
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EXTENSIONS
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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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