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A257827 Positive integers whose square is the sum of 96 consecutive squares. 3
652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724, 60988, 68356, 74852, 97348, 178132, 231668, 253684, 284332, 603716, 676652, 740956, 963644, 1763324, 2293276, 2511212, 2814596, 5976172, 6698164, 7334708 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-192*y^2-18240*y-580640 = 0.
LINKS
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
Sequence in context: A110850 A257715 A048915 * A261552 A002232 A127029
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 10 2015
STATUS
approved

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)