The On-Line Encyclopedia of Integer Sequences (OEIS)

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A133283

Numbers n such that 30*n^2 + 6 is a square.
(history; published version)

#29 by Charles R Greathouse IV at Thu Sep 08 08:45:31 EDT 2022

PROG

(MAGMAMagma) I:=[1, 23]; [n le 2 select I[n] else 22*Self(n-1) - Self(n-2): n in [1..20]]; // G. C. Greubel, Jan 13 2020

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#28 by Susanna Cuyler at Tue Jan 14 09:59:38 EST 2020

STATUS

proposed

approved

#27 by Michel Marcus at Tue Jan 14 01:21:56 EST 2020

STATUS

editing

proposed

#26 by Michel Marcus at Tue Jan 14 01:21:51 EST 2020

PROG

(MAGMA) I:=[1, 23]; [n le 2 select I[n] else 22*Self(n-1) - Self(n-2): n in [1..3020]]; // G. C. Greubel, Jan 13 2020

STATUS

proposed

editing

#25 by G. C. Greubel at Mon Jan 13 23:40:42 EST 2020

STATUS

editing

proposed

#24 by G. C. Greubel at Mon Jan 13 23:40:06 EST 2020

NAME

Numbers n such that 30*n^2 + 6 is a square.

FORMULA

a(n+2) = 22*a(n+1) - a(n) ; a(n+1) = 11*a(n) + 2*sqrt(30*a(n)^2 + 6)^0.5.

a(n) = A077421(n) + A077421(n-1). - R. J. Mathar, Feb 19 2016

a(n) = Chebyshev(n-1, 11) + Chebyshev(n-2, 11). - G. C. Greubel, Jan 13 2020

MATHEMATICA

Table[n /. {ToRules[Reduce[n > 0 && k >= 0 && 30*n^2+6 == k^2, n, Integers] /. C[1] -> c]} // Simplify, {c, 1, 1620}] // Flatten // Union (* Jean-François Alcover, Dec 19 2013 *)

Rest@ CoefficientList[Series[x (1 + x)/(1 - 22 x 22x+ x^2), {x, 0, 1620}], x] (* Michael De Vlieger, Jul 14 2016 *)

Table[ChebyshevU[n-1, 11] + ChebyshevU[n-2, 11], {n, 20}] (* G. C. Greubel, Jan 13 2020 *)

PROG

(PARI) vector(20, n, polchebyshev(n-1, 2, 11) + polchebyshev(n-2, 2, 11) ) \\ G. C. Greubel, Jan 13 2020

(MAGMA) I:=[1, 23]; [n le 2 select I[n] else 22*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 13 2020

(Sage) [chebyshev_U(n-1, 11) + chebyshev_U(n-2, 11) for n in (1..20)] # G. C. Greubel, Jan 13 2020

(GAP) a:=[1, 23];; for n in [3..20] do a[n]:=22*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Jan 13 2020

STATUS

approved

editing

#23 by Harvey P. Dale at Fri Sep 22 19:40:54 EDT 2017

STATUS

editing

approved

#22 by Harvey P. Dale at Fri Sep 22 19:40:50 EDT 2017

MATHEMATICA

LinearRecurrence[{22, -1}, {1, 23}, 20] (* Harvey P. Dale, Sep 22 2017 *)

STATUS

approved

editing

#21 by Alois P. Heinz at Thu Jul 14 17:44:36 EDT 2016

STATUS

reviewed

approved

#20 by Michel Marcus at Thu Jul 14 17:02:14 EDT 2016

STATUS

proposed

reviewed