

A159669


Expansion of x*(x + 1)/(x^2  28*x + 1).


3



1, 29, 811, 22679, 634201, 17734949, 495944371, 13868707439, 387827863921, 10845311482349, 303280893641851, 8481019710489479, 237165271000063561, 6632146568291290229, 185462938641156062851, 5186330135384078469599, 145031780852113041085921
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OFFSET

1,2


COMMENTS

Previous name was: The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 13*n(j)+1=a(j)*a(j) and 15*n(j)+1=b(j)*b(j) with positive integer numbers.


REFERENCES

Mohammad K. Azarian, Diophantine Pair, Problem B881, Fibonacci Quarterly, Vol. 37, No. 3, August 1999, pp. 277278. Solution published in Vol. 38, No. 2, May 2000, pp. 183184.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index to sequences with linear recurrences with constant coefficients, signature (28,1).


FORMULA

The a(j) recurrence is a(1)=1; a(2)=27; a(t+2)=28*a(t+1)a(t)
resulting in terms 1, 27, 755, 21113... (A159668)
The b(j) recurrence is b(1)=1; b(2)=29; b(t+2)=28*b(t+1)b(t)
resulting in terms 1, 29, 811, 22679... (this sequence)
The n(j) recurrence is n(0)=n(1)=0; n(2)=56; n(t+3)=783*(n(t+2)n(t+1))+n(t)
resulting in terms 0, 0, 56, 43848, 34289136... (A159673)
G.f.: x*(x+1)/(x^228*x+1).  Vincenzo Librandi, Feb 26 2014


MAPLE

for a from 1 by 2 to 100000 do b:=sqrt((15*a*a2)/13): if (trunc(b)=b) then
n:=(a*a1)/13: La:=[op(La), a]:Lb:=[op(Lb), b]:Ln:=[op(Ln), n]: endif: enddo:


MATHEMATICA

CoefficientList[Series[(x + 1)/(x^2  28 x + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 26 2014 *)


PROG

(PARI) Vec(x*(x+1)/(x^228*x+1) + O(x^100)) \\ Colin Barker, Feb 24 2014


CROSSREFS

A157456, A159668, A159673.
Sequence in context: A135995 A046850 A180844 * A162831 A163207 A163549
Adjacent sequences: A159666 A159667 A159668 * A159670 A159671 A159672


KEYWORD

nonn,easy


AUTHOR

Paul Weisenhorn, Apr 19 2009


EXTENSIONS

More terms from, and new name by Colin Barker, Feb 24 2014


STATUS

approved



