OFFSET
1,1
COMMENTS
Positive integers y in the solutions to 2*x^2-46*y^2-1012*y-7590 = 0.
All sequences of this type (i.e. sequences with fixed offset k, and a discernible pattern: k=0...22 for this sequence, k=0..1 for A001652, k=0...10 for A106521) can be continued using a formula such as x(n) = a*x(n-p) - x(n-2p) + b, where a and b are various constants, and p is the period of the series. Alternatively 'p' can be considered the number of concurrent series. - Daniel Mondot, Aug 05 2016
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,48,-48,-1,1).
FORMULA
a(n) = a(n-1)+48*a(n-2)-48*a(n-3)-a(n-4)+a(n-5) for n>5.
G.f.: x*(7+10*x+528*x^2-10*x^3-29*x^4) / ((1-x)*(1-48*x^2+x^4)).
a(1)=7, a(2)=17, a(3)=881, a(4)=1351, a(n) = 48*a(n-2)-a(n-4)+506. - Daniel Mondot, Aug 05 2016
EXAMPLE
7 is in the sequence because sum(k=7, 29, k^2) = 8464 = 92^2.
MATHEMATICA
LinearRecurrence[{1, 48, -48, -1, 1}, {7, 17, 881, 1351, 42787}, 30] (* Harvey P. Dale, May 21 2024 *)
PROG
(PARI) Vec(x*(7+10*x+528*x^2-10*x^3-29*x^4)/((1-x)*(1-48*x^2+x^4)) + O(x^30))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 27 2016
STATUS
approved