A257827 -id:A257827 - cp's OEIS frontend

A257828 Positive integers whose square is the sum of 97 consecutive squares.

679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831, 10253011689091642135, 24386783991798773338556, 58003955471481693294113311, 1287975802673112210113634031, 3063449905150311732357259611836, 7286414311424213782299531873117895

Offset: 1

Colin Barker, May 10 2015

Positive integers x in the solutions to 2*x^2-194*y^2-18624*y-599072 = 0.

			679 is in the sequence because 679^2 = 461041 = 15^2+16^2+...+111^2.

Colin Barker, Table of n, a(n) for n = 1..370
Index entries for linear recurrences with constant coefficients, signature (0,0,125619266,0,0,-1).

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823-A257826, A257827.

I:=[679,1545404,3675742735,81619738879, 194132514608060,461744104375531831]; [n le 6 select I[n] else 125619266*Self(n-3)-Self(n-6): n in [1..20]]; // Vincenzo Librandi, May 11 2015

LinearRecurrence[{0, 0, 125619266, 0, 0, -1}, {679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831}, 30] (* Vincenzo Librandi, May 11 2015 *)
Rest[CoefficientList[Series[-679x(x-1)(x^4+2277x^3+5415742x^2+ 2277x+1)/ (x^6-125619266x^3+1),{x,0,15}],x]] (* Harvey P. Dale, Aug 02 2021 *)

Vec(-679*x*(x-1)*(x^4+2277*x^3+5415742*x^2+2277*x+1) / (x^6-125619266*x^3+1) + O(x^100))

a(n) = 125619266*a(n-3)-a(n-6).

G.f.: -679*x*(x-1)*(x^4+2277*x^3+5415742*x^2+2277*x+1) / (x^6-125619266*x^3+1).

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

Original entry on oeis.org

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).

cp's OEIS Frontend

A257828 Positive integers whose square is the sum of 97 consecutive squares.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula