A182755 Expansion of (1+35*x)/(1-90*x^2).

1, 35, 90, 3150, 8100, 283500, 729000, 25515000, 65610000, 2296350000, 5904900000, 206671500000, 531441000000, 18600435000000, 47829690000000, 1674039150000000, 4304672100000000, 150663523500000000, 387420489000000000, 13559717115000000000, 34867844010000000000

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• easy

Comments

a(1) = 1, a(2) = 35, for n >= 3; a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + h] * [a(n-1) + h]] / [a(n-2) * a(n-1) * h] is an integer (= 130). (conjectured)

10^(floor((n - 1)/2)) | a(n), for n>=1. - G. C. Greubel, Jan 11 2018

Examples

			For n = 4; a(2) = 35, a(3) = 90, a(4) = 3150 before [(35+90)*(35+3150)*(90+3150)]  / (35*90*3150) = 130.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,90).

Crossrefs

Cf. A182751, A182752, A182753, A182754, A182756, A182757, A038754.

Programs

Magma

I:=[1,35]; [n le 2 select I[n] else 90*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 11 2018

Mathematica

LinearRecurrence[{0,90}, {1,35}, 50] (* or *) CoefficientList[Series[(1 + 35*x)/(1-90*x^2), {x,0,50}], x] (* G. C. Greubel, Jan 11 2018 *)

PARI

Vec((1+35*x)/(1-90*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(2n) = 35* a(2n-1), a(2n+1) = (18/7) * a(2n).

a(2n) = 35*90^(n-1), a(2n+1) = 90^n.

Extensions

Terms a(12) onward added by G. C. Greubel, Jan 11 2018