A103201 a(1) = 11, a(2) = 19, a(3) = 89, a(4) = 151; for n >= 5, a(n) = sqrt(a(n-4)^2 + 60*a(n-2)^2 + 4*a(n-2)*sqrt(210 + 15*a(n-4)^2)).

11, 19, 89, 151, 701, 1189, 5519, 9361, 43451, 73699, 342089, 580231, 2693261, 4568149, 21203999, 35964961, 166938731, 283151539, 1314305849, 2229247351, 10347508061, 17550827269, 81465758639, 138177370801, 641378561051

Offset: 1

Author

K. S. Bhanu and M. N. Deshpande, Mar 24 2005

Keywords

• nonn

References

• K. S. Bhanu (bhanu_105(AT)yahoo.com) and M. N. Deshpande, An interesting sequence of quadruples and related open problems, Institute of Sciences, Nagpur, India, Preprint, 2005.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,8,0,-1).

Crossrefs

This is the sequence b(n) defined in A103200. Bhanu and Deshpande ask for a proof that the terms of the sequence are always integers.

Cf. A103200.

Programs

GAP

a:=[11,19,89,151];; for n in [5..30] do a[n]:=8*a[n-2]-a[n-4]; od; a; # G. C. Greubel, May 24 2019

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(11+19*x+x^2-x^3)/(1-8*x^2+x^4) )); // G. C. Greubel, May 24 2019

Maple

b[1]:=11:b[2]:=19:b[3]:=89:b[4]:=151: for n from 5 to 28 do b[n]:=sqrt(b[n-4]^2+60*b[n-2]^2+4*b[n-2]*sqrt(210+15*b[n-4]^2)) od:seq(b[n],n=1..28); # Emeric Deutsch, Apr 13 2005

Mathematica

LinearRecurrence[{0, 8, 0, -1}, {11, 19, 89, 151}, 30] (* Georg Fischer, May 24 2019 *)

PARI

my(x='x+O('x^30)); Vec(x*(11+19*x+x^2-x^3)/(1-8*x^2+x^4)) \\ G. C. Greubel, May 24 2019

Sage

a=(x*(11+19*x+x^2-x^3)/(1-8*x^2+x^4)).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, May 24 2019

Formula

G.f.: x*(11 + 19*x + x^2 - x^3)/(1 - 8*x^2 + x^4). - Georg Fischer, May 24 2019

Extensions

More terms from Pierre CAMI and Emeric Deutsch, Apr 13 2005