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A038761
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a(n)=6a(n-1)-a(n-2), n >= 2, a(0)=1, a(1)=9.
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15
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1, 9, 53, 309, 1801, 10497, 61181, 356589, 2078353, 12113529, 70602821, 411503397, 2398417561, 13979001969, 81475594253, 474874563549, 2767771787041, 16131756158697, 94022765165141, 548004834832149
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Bisection of A048654. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 24 2004
A Pellian-related sequence.
a(n)={9*([3+2*sqrt(2)]^n -[3-2*sqrt(2)]^n)-([3+2*sqrt(2)]^(n-1) - [3-2*sqrt(2)]^(n-1))}/(4*sqrt(2)).
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.
M. J. DeLeon, Pell's Equation and Pell Number Triples, Fib. Quart., 14(1976), pp. 456-460.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
| A038761 = sqrt{2*(A038762)^2-14}/2.
For n>1, a(n)-4a(n-1)=A001541(n)-A001542(n-2); e.g. 309-4*53=97=99-2 - Charlie Marion (charliem(AT)bestweb.net), Nov 12 2003
For n>0, a(n)=A046090(n)+A001653(n)+A001652(n-1)=A055997(n+1)+A001652(n-1); e.g., 309=120+169+20 - Charlie Marion (charliemath(AT)optonline.net), Oct 11 2006
G.f.: (1+3*x)/(1-6*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]
a(n)=third binomial transform of 1,6,8,48,64,384 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009]
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MAPLE
| a[0]:=1: a[1]:=9: for n from 2 to 26 do a[n]:=6*a[n-1]-a[n-2] od: seq(a[n], n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 26 2006
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MATHEMATICA
| LinearRecurrence[{6, -1}, {1, 9}, 40] (* Vincenzo Librandi, Nov 16 2011 *)
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PROG
| (MAGMA) I:=[1, 9]; [n le 2 select I[n] else 6*Self(n-1)-Self(n-2): n in [1..40]]; // Vincenzo Librandi, Nov 16 2011
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CROSSREFS
| Cf. A038762.
Sequence in context: A202514 A122588 A005025 * A003698 A001688 A144040
Adjacent sequences: A038758 A038759 A038760 * A038762 A038763 A038764
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KEYWORD
| easy,nonn
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AUTHOR
| Barry E. Williams, May 02 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 04 2000
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