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A257823 Positive integers whose square is the sum of 59 consecutive squares. 11
413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727, 452101247, 587437689, 9744411267, 12661399351, 479226895309, 622683396153, 10329066750171, 13421071367333, 507980056926293, 660043812484491, 10948801010769993, 14226322987973629, 538458381114975271 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Positive integers x in the solutions to 2*x^2-118*y^2-6844*y-133458 = 0.
LINKS
FORMULA
a(n) = 1060*a(n-4)-a(n-8).
G.f.: -59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1).
EXAMPLE
413 is in the sequence because 413^2 = 170569 = 22^2+23^2+...+80^2.
MATHEMATICA
LinearRecurrence[{0, 0, 0, 1060, 0, 0, 0, -1}, {413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727}, 30] (* Vincenzo Librandi, May 11 2015 *)
PROG
(PARI) Vec(-59*x*(x-1)*(7*x^6+16*x^5+163*x^4+354*x^3+163*x^2+16*x+7) / (x^8-1060*x^4+1) + O(x^100))
(Magma) I:=[413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727]; [n le 8 select I[n] else 1060*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, May 11 2015
CROSSREFS
Sequence in context: A234185 A282127 A344119 * A250901 A205755 A331825
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 10 2015
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)