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Search: id:A084158
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| 0, 1, 5, 30, 174, 1015, 5915, 34476, 200940, 1171165, 6826049, 39785130, 231884730, 1351523251, 7877254775, 45912005400, 267594777624, 1559656660345, 9090345184445, 52982414446326, 308804141493510, 1799842434514735
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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May be called Pell triangles.
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FORMULA
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a(n)=((sqrt(2)+1)^(2n+1)-(sqrt(2)-1)^(2n+1)-2(-1)^n)/16.
a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3). - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Sep 02 2006; corrected by Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 29 2008
a(n) = (-1/8)*(-1)^n + (( sqrt(2)+1)/16)*(3+2*sqrt(2))^n + ((-sqrt(2)+1)/16)*(3-2*sqrt(2))^n. - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 30 2008
(a(n)-a(n-1))^(1/2) = A000129(n) - Antonio A. Olivares (olivares14031(AT)yahoo.com), Mar 30 2008
O.g.f.: x/((1+x)(x^2-6*x+1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 18 2008
a(n)=A041011(n)*A041011(n+1). - R. Guy (rkg(AT)cpsc.ucalgary.ca), May 18 2008
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MAPLE
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with(combinat): a:=n->fibonacci(n, 2)*fibonacci(n-1, 2)/2: seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008
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CROSSREFS
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Cf. A084159, A084175, A001654.
Cf. a001652.
Sequence in context: A003731 A055838 A094972 this_sequence A111469 A057088 A105481
Adjacent sequences: A084155 A084156 A084157 this_sequence A084159 A084160 A084161
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 18 2003
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