login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159680 The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 9*n(j)+1=a(j)*a(j) and 11*n(j)+1=b(j)*b(j) with positive integer numbers. 1
0, 40, 15960, 6352080, 2528111920, 1006182192120, 400457984351880, 159381271589856160, 63433345634778399840, 25246312181370213280200, 10047968814839710107119800, 3999066341994023252420400240, 1591618356144806414753212175760, 633460106679290959048526025552280 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..350

Index entries for linear recurrences with constant coefficients, signature (399,-399,1).

FORMULA

The a(j) recurrence is a(1)=1; a(2)=19; a(t+2)=20*a(t+1)-a(t)

resulting in terms 1, 19, 379, 7561

The b(j) recurrence is b(1)=1; b(2)=21; b(t+2)=20*b(t+1)-b(t)

resulting in terms 1, 21, 419, 8359

The n(j) recurrence is n(0)=n(1)=0; n(2)=40; n(t+3)=399*(n(t+2)-n(t+1))+n(t)

resulting in terms 0, 0, 40, 15960, 6352080 as listed above

G.f.: -40*x^2/((x-1)*(x^2-398*x+1)). - R. J. Mathar, Apr 20 2009

a(n) = (-20+(10+3*sqrt(11))*(199+60*sqrt(11))^(-n)+(10-3*sqrt(11))*(199+60*sqrt(11))^n)/198. - Colin Barker, Jul 26 2016

MAPLE

for a from 1 by 2 to 100000 do b:=sqrt((9*a*a-2)/7): if (trunc(b)=b) then

n:=(a*a-1)/7: La:=[op(La), a]:Lb:=[op(Lb), b]:Ln:=[op(Ln), n]: end if: end do:

MATHEMATICA

CoefficientList[Series[40*x^2/((1-x)*(x^2-398*x+1)), {x, 0, 50}], x] (* or *) LinearRecurrence[{399, -399, 1}, {0, 40, 15960}, 50] (* G. C. Greubel, Jun 03 2018 *)

PROG

(PARI) a(n) = round((-20+(10+3*sqrt(11))*(199+60*sqrt(11))^(-n)+(10-3*sqrt(11))*(199+60*sqrt(11))^n)/198) \\ Colin Barker, Jul 26 2016

(PARI) concat(0, Vec(-40*x^2/((x-1)*(x^2-398*x+1)) + O(x^20))) \\ Colin Barker, Jul 26 2016

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(40*x^2/((1-x)*(x^2-398*x+1)))); // G. C. Greubel, Jun 03 2018

CROSSREFS

Cf. A157456, A075839, A083043.

Sequence in context: A210347 A221391 A279578 * A240628 A159390 A204682

Adjacent sequences:  A159677 A159678 A159679 * A159681 A159682 A159683

KEYWORD

nonn,easy

AUTHOR

Paul Weisenhorn, Apr 19 2009

EXTENSIONS

More terms from R. J. Mathar, Apr 20 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)