The On-Line Encyclopedia of Integer Sequences (OEIS)

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A098303

Member r=18 of the family of Chebyshev sequences S_r(n) defined in A092184.
(history; published version)

#12 by Michel Marcus at Wed Feb 24 04:14:58 EST 2021

STATUS

reviewed

approved

#11 by Joerg Arndt at Wed Feb 24 02:47:55 EST 2021

STATUS

proposed

reviewed

#10 by Michel Marcus at Tue Feb 23 22:46:15 EST 2021

STATUS

editing

proposed

#9 by Michel Marcus at Tue Feb 23 22:46:10 EST 2021

LINKS

<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-17,1).

FORMULA

a(n) = (T(n, 8)-1)/7 with Chebyshev's polynomials of the first kind evaluated at x=8: T(n, 8)=A001081(n)= ((8+3*sqrt(7))^n + (8-3*sqrt(7))^n)/2.

a(n) = 16*a(n-1) - a(n-2) + 2, n>=2, a(0)=0, a(1)=1.

a(n) = 17*a(n-1) - 17*a(n-2) + a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=18.

STATUS

proposed

editing

#8 by Michael De Vlieger at Tue Feb 23 18:32:49 EST 2021

STATUS

editing

proposed

#7 by Michael De Vlieger at Tue Feb 23 18:32:47 EST 2021

LINKS

Michael De Vlieger, <a href="/A098303/b098303.txt">Table of n, a(n) for n = 0..832</a>

S. Barbero, U. Cerruti, and N. Murru, <a href="http://www.seminariomatematico.polito.it/rendiconti/78-1/BarberoCerrutiMurru.pdf">On polynomial solutions of the Diophantine equation (x + y - 1)^2 = wxy</a>, Rendiconti Sem. Mat. Univ. Pol. Torino (2020) Vol. 78, No. 1, 5-12.

MATHEMATICA

LinearRecurrence[{# - 1, -# + 1, 1}, {0, 1, #}, 17] &[18] (* Michael De Vlieger, Feb 23 2021 *)

STATUS

approved

editing

#6 by Charles R Greathouse IV at Fri Oct 12 14:40:22 EDT 2012

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004

Wolfdieter Lang, Oct 18 2004

Discussion

Fri Oct 12

14:40

OEIS Server: https://oeis.org/edit/global/1838

#5 by Russ Cox at Sun Jul 10 18:19:13 EDT 2011

LINKS

<a href="/Sindx_index/Ch.html#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

Discussion

Sun Jul 10

18:19

OEIS Server: https://oeis.org/edit/global/28

#4 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

<a href="/Sindx_Ch.html#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

KEYWORD

nonn,easy,new

#3 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

LINKS

<a href="http://www.research.att.com/~njas/sequences/Sindx_Ch.html#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

KEYWORD

nonn,easy,new