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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

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1060,0,0,0,-1).

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

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257824-A257828.

Sequence in context: A234190 A234185 A282127 * A250901 A205755 A250945

Adjacent sequences:  A257820 A257821 A257822 * A257824 A257825 A257826

KEYWORD

nonn,easy

AUTHOR

Colin Barker, May 10 2015

STATUS

approved

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Last modified February 18 19:50 EST 2019. Contains 320262 sequences. (Running on oeis4.)