OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-192*y^2-18240*y-580640 = 0.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,10,0,0,0,0,0,0,0,-1).
FORMULA
a(n) = 10*a(n-8) -a(n-16).
G.f.: -4*x*(89*x^15 +83*x^14 +79*x^13 +71*x^12 +71*x^11 +79*x^10 +83*x^9 +89*x^8 -727*x^7 -649*x^6 -593*x^5 -457*x^4 -253*x^3 -197*x^2 -181*x-163) / (x^16 -10*x^8 +1).
EXAMPLE
652 is in the sequence because 652^2 = 425104 = 13^2+14^2+...+108^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -1}, {652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724}, 40] (* Vincenzo Librandi, May 11 2015 *)
PROG
(PARI)
Vec(-4*x*(89*x^15 +83*x^14 +79*x^13 +71*x^12 +71*x^11 +79*x^10 +83*x^9 +89*x^8 -727*x^7 -649*x^6 -593*x^5 -457*x^4 -253*x^3 -197*x^2 -181*x -163) / (x^16-10*x^8+1) + O(x^100))
(Magma) I:=[652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724]; [n le 16 select I[n] else 10*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, May 11 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 10 2015
STATUS
approved