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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| May be called Pell triangles.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..500
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FORMULA
| a(n)=((sqrt(2)+1)^(2*n+1)-(sqrt(2)-1)^(2*n+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
a(n)=6*a(n-1)-a(n-2)-(-1)^n. a(n)=7*(a(n-1)-a(n-2))+a(n-3)-2*(-1)^n. - Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Aug 30 2008
In general, for n>k+1, a(n+k) = A003499(k+1)*a(n-1) - a(n-k-2) - (-1)^n A000129(k+1)^2. - Charlie Marion, Jan 04 2012
For n>0, a(2n-1)*a(2n+1) = oblong(a(2n)); a(2n)*a(2n+2) = oblong(a(2n+1)-1). - Charlie Marion, Jan 09 2012
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MAPLE
| 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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MATHEMATICA
| LinearRecurrence[{5, 5, -1}, {0, 1, 5}, 30] (* From Harvey P. Dale, Sep 07 2011 *)
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PROG
| (MAGMA) [Floor(((Sqrt(2)+1)^(2*n+1)-(Sqrt(2)-1)^(2*n+1)-2*(-1)^n)/16): n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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CROSSREFS
| Cf. A084159, A084175, A001654.
Cf. a001652.
Sequence in context: A003731 A055838 A094972 * A111469 A057088 A156195
Adjacent sequences: A084155 A084156 A084157 * A084159 A084160 A084161
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 18 2003
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