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A257826 Positive integers whose square is the sum of 88 consecutive squares. 4
2222, 2530, 39358, 55990, 872938, 994598, 15506810, 22059818, 343935350, 391869082, 6109643782, 8691512302, 135509654962, 154395423710, 2407184143298, 3424433787170, 53390460119678, 60831405072658, 948424442815630, 1349218220632678, 21035705777498170 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Positive integers x in the solutions to 2*x^2-176*y^2-15312*y-446600 = 0.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,394,0,0,0,-1).

FORMULA

a(n) = 394*a(n-4)-a(n-8).

G.f.: -22*x*(11*x^7+11*x^6+101*x^5+115*x^4-2545*x^3-1789*x^2-115*x-101) / (x^8-394*x^4+1).

EXAMPLE

2222 is in the sequence because 2222^2 = 4937284 = 192^2+193^2+...+279^2.

MATHEMATICA

LinearRecurrence[{0, 0, 0, 394, 0, 0, 0, -1}, {2222, 2530, 39358, 55990, 872938, 994598, 15506810, 22059818}, 40] (* Vincenzo Librandi, May 11 2015 *)

PROG

(PARI) Vec(-22*x*(11*x^7+11*x^6+101*x^5+115*x^4-2545*x^3-1789*x^2-115*x-101) / (x^8-394*x^4+1) + O(x^100))

(MAGMA) I:=[2222, 2530, 39358, 55990, 872938, 994598, 15506810, 22059818]; [n le 8 select I[n] else 394*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, May 11 2015

CROSSREFS

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823-A257825, A257827, A257828.

Sequence in context: A166580 A091189 A046443 * A043500 A118116 A053395

Adjacent sequences:  A257823 A257824 A257825 * A257827 A257828 A257829

KEYWORD

nonn,easy

AUTHOR

Colin Barker, May 10 2015

STATUS

approved

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Last modified July 25 16:03 EDT 2021. Contains 346291 sequences. (Running on oeis4.)