A182753 Expansion of (1 + 14*x)/(1 - 35*x^2).

1, 14, 35, 490, 1225, 17150, 42875, 600250, 1500625, 21008750, 52521875, 735306250, 1838265625, 25735718750, 64339296875, 900750156250, 2251875390625, 31526255468750, 78815638671875, 1103418941406250, 2758547353515625, 38619662949218750, 96549157373046875

Offset: 1

Author

Jaroslav Krizek, Nov 27 2010

Keywords

• nonn
• easy

Comments

a(1) = 1, a(2) = 14, 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 (= 54).

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

Examples

			For n = 5; a(3) = 35, a(4) = 490, a(5) = 1225 before [(35+490)*(35+1225)*(490+1225)]  / (35*490*1225) = 54.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,35).

Crossrefs

Cf. A182751, A182752, A182754, A182755, A182756, A182757.

Programs

Magma

I:=[1,14]; [n le 2 select I[n] else 35*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 11 2018

Mathematica

LinearRecurrence[{0, 35}, {1, 14}, 30] (* or *) CoefficientList[Series[(1 + 14*x)/(1-35*x^2), {x,0,50}], x] (* G. C. Greubel, Jan 11 2018 *)

PARI

Vec((1+14*x)/(1-35*x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 25 2012

Formula

a(2n) = 14 * a(2n-1), a(2n+1) = (5/2) * a(2n).

a(2n) = 14*35^(n-1), a(2n+1) = 35^n.

Extensions

Terms a(15) onward added by G. C. Greubel, Jan 11 2018