PROG
(MAGMAMagma) m:=13; I:=[0, 1]; [n le 2 select I[n] else 2*m*Self(n-1) -Self(n-2): n in [1..20]]; // G. C. Greubel, Dec 22 2019
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Revision History for A097309
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
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COMMENTS
For positive n, a(n) equals the permanent of the n X n tridiagonal matrix with 26's along the main diagonal, and i's along the superdiagonal and the subdiagonal (i is the imaginary unit). - _John M. Campbell, _, Jul 08 2011
For n>=1, a(n) equals the number of 01-avoiding words of length n-1 on alphabet {0,1,...,25}. _- _Milan Janjic_, Jan 25 2015
LINKS
Pablo Lam-Estrada, Myriam Rosalía Maldonado-Ramírez, José Luis López-Bonilla, and Fausto Jarquín-Zárate, <a href="https://arxiv.org/abs/1904.13002">The sequences of Fibonacci and Lucas for each real quadratic fields Q(Sqrt(d))</a>, arXiv:1904.13002 [math.NT], 2019.
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FORMULA
a(n) = 26*a(n-1) - a(n-2), a(-1)=0, a(0)=1. - Philippe Deléham, Nov 18 2008
a(n) = Sum_{k, =0<=k<=..n} A101950(n,k)*25^k. - Philippe Deléham, Feb 10 2012
MAPLE
seq( simplify(ChebyshevU(n, 13)), n=-1..20); # G. C. Greubel, Dec 22 2019
MATHEMATICA
lst={}; Do[AppendToTable[lst, GegenbauerC[n, 1, 13]], , {n, 0, 8^2-1, 20}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 11 2008 *)
ChebyshevU[Range[22] -2, 13] (* G. C. Greubel, Dec 22 2019 *)
PROG
(Sage) [chebyshev_U(n, 13) for n in (-1..20)] # G. C. Greubel, Dec 22 2019
(PARI) vector( 22, n, polchebyshev(n-2, 2, 13) ) \\ G. C. Greubel, Dec 22 2019
(MAGMA) m:=13; I:=[0, 1]; [n le 2 select I[n] else 2*m*Self(n-1) -Self(n-2): n in [1..20]]; // G. C. Greubel, Dec 22 2019
(GAP) m:=13;; a:=[0, 1];; for n in [3..20] do a[n]:=2*m*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 22 2019
CROSSREFS
Chebyshev sequence U(n, m): A000027 (m=1), A001353 (m=2), A001109 (m=3), A001090 (m=4), A004189 (m=5), A004191 (m=6), A007655 (m=7), A077412 (m=8), A049660 (m=9), A075843 (m=10), A077421 (m=11), A077423 (m=12), this sequence (m=13), A097311 (m=14), A097313 (m=15), A029548 (m=16), A029547 (m=17), A144128 (m=18), A078987 (m=19), A097316 (m=33).
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PROG
(Sage) [lucas_number1(n, 26, 1) for n in xrangerange(0, 20)] # Zerinvary Lajos, Jun 25 2008
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