A257825 -id:A257825 - cp's OEIS frontend

A257826 Positive integers whose square is the sum of 88 consecutive squares.

2222, 2530, 39358, 55990, 872938, 994598, 15506810, 22059818, 343935350, 391869082, 6109643782, 8691512302, 135509654962, 154395423710, 2407184143298, 3424433787170, 53390460119678, 60831405072658, 948424442815630, 1349218220632678, 21035705777498170

Offset: 1

Colin Barker, May 10 2015

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

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

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).

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

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

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

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))

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).

A257824 Positive integers whose square is the sum of 73 consecutive squares.

Original entry on oeis.org

4088, 23360, 1582640, 9047912, 18642443912, 106578370640, 7220791811360, 41281080400088, 85056113063608088, 486263602888235360, 32944848197744794640, 188344846763231651912, 388068345740467131839912, 2218576715650261475158640, 150310804012507009263599360

Offset: 1

Colin Barker, May 10 2015

Positive integers x in the solutions to 2*x^2-146*y^2-10512*y-254040 = 0.

			4088 is in the sequence because 4088^2 = 16711744 = 442^2+443^2+...+514^2.

Colin Barker, Table of n, a(n) for n = 1..600
Index entries for linear recurrences with constant coefficients, signature (0,0,0,4562498,0,0,0,-1).

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

I:=[4088,23360,1582640,9047912,18642443912, 106578370640,7220791811360,41281080400088]; [n le 8 select I[n] else 4562498*Self(n-4)-Self(n-8): n in [1..20]]; // Vincenzo Librandi, May 11 2015

LinearRecurrence[{0, 0, 0, 4562498, 0, 0, 0, -1}, {4088, 23360, 1582640, 9047912, 18642443912, 106578370640, 7220791811360, 41281080400088}, 40] (* Vincenzo Librandi, May 11 2015 *)

Vec(-584*x*(x-1)*(7*x^6+47*x^5+2757*x^4+18250*x^3+2757*x^2+47*x+7) / ((x^4-2136*x^2-1)*(x^4+2136*x^2-1)) + O(x^100))

a(n) = 4562498*a(n-4)-a(n-8).

G.f.: -584*x*(x-1)*(7*x^6+47*x^5+2757*x^4+18250*x^3+2757*x^2+47*x+7) / ((x^4-2136*x^2-1)*(x^4+2136*x^2-1)).

cp's OEIS Frontend

A257826 Positive integers whose square is the sum of 88 consecutive squares.

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