cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

679, 1545404, 3675742735, 81619738879, 194132514608060, 461744104375531831, 10253011689091642135, 24386783991798773338556, 58003955471481693294113311, 1287975802673112210113634031, 3063449905150311732357259611836, 7286414311424213782299531873117895
Offset: 1

Views

Author

Colin Barker, May 10 2015

Keywords

Comments

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

Examples

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

Links

Crossrefs

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

Programs

  • Magma
    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
  • Mathematica
    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 *)
  • PARI
    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))

Formula

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).

A257825 Positive integers whose square is the sum of 74 consecutive squares.

Original entry on oeis.org

2257, 2849, 21941, 27713, 604765, 763865, 16669573, 21054961, 162316669, 205018517, 4474051285, 5651073085, 123321498797, 155764598629, 1200818695321, 1516726961053, 33099030801665, 41806637918965, 912332431430633, 1152346479602381, 8883656545668089
Offset: 1

Views

Author

Colin Barker, May 10 2015

Keywords

Comments

Positive integers x in the solutions to 2*x^2-148*y^2-10804*y-264698 = 0.

Examples

			2257 is in the sequence because 2257^2 = 5094049 = 225^2+226^2+...+298^2.

Links

Crossrefs

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823, A257824, A257826-A257828.

Programs

  • Magma
    I:=[2257,2849,21941,27713,604765,763865,16669573, 21054961,162316669,205018517,4474051285,5651073085]; [n le 12 select I[n] else 7398*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, May 11 2015
  • Mathematica
     LinearRecurrence[{0, 0, 0, 0, 0, 7398, 0, 0, 0, 0, 0, -1}, {2257, 2849, 21941, 27713, 604765, 763865, 16669573, 21054961, 162316669, 205018517, 4474051285, 5651073085}, 40] (* Vincenzo Librandi, May 11 2015 *)
  • PARI
    Vec(-37*x*(5*x^11+5*x^10+61*x^9+77*x^8+593*x^7+749*x^6-20645*x^5-16345*x^4-749*x^3-593*x^2-77*x-61) / ((x^6-86*x^3-1)*(x^6+86*x^3-1)) + O(x^100))

Formula

a(n) = 7398*a(n-6)-a(n-12).
G.f.: -37*x*(5*x^11+5*x^10+61*x^9+77*x^8+593*x^7+749*x^6-20645*x^5-16345*x^4-749*x^3-593*x^2-77*x-61) / ((x^6-86*x^3-1)*(x^6+86*x^3-1)).

A257827 Positive integers whose square is the sum of 96 consecutive squares.

Original entry on oeis.org

652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724, 60988, 68356, 74852, 97348, 178132, 231668, 253684, 284332, 603716, 676652, 740956, 963644, 1763324, 2293276, 2511212, 2814596, 5976172, 6698164, 7334708
Offset: 1

Views

Author

Colin Barker, May 10 2015

Keywords

Comments

Positive integers x in the solutions to 2*x^2-192*y^2-18240*y-580640 = 0.

Examples

			652 is in the sequence because 652^2 = 425104 = 13^2+14^2+...+108^2.

Links

Crossrefs

Cf. A001653, A180274, A218395, A257761, A257765, A257767, A257780, A257781, A257823-A257826, A257828.

Programs

  • Magma
    I:=[652,724,788,1012,1828,2372,2596,2908,6164,6908, 7564,9836,17996,23404,25628,28724]; [n le 16 select I[n] else 10*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, May 11 2015
  • Mathematica
    LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -1}, {652, 724, 788, 1012, 1828, 2372, 2596, 2908, 6164, 6908, 7564, 9836, 17996, 23404, 25628, 28724}, 40] (* Vincenzo Librandi, May 11 2015 *)
  • PARI
    Vec(-4*x*(89*x^15 +83*x^14 +79*x^13 +71*x^12 +71*x^11 +79*x^10 +83*x^9 +89*x^8 -727*x^7 -649*x^6 -593*x^5 -457*x^4 -253*x^3 -197*x^2 -181*x -163) / (x^16-10*x^8+1) + O(x^100))

Formula

a(n) = 10*a(n-8) -a(n-16).
G.f.: -4*x*(89*x^15 +83*x^14 +79*x^13 +71*x^12 +71*x^11 +79*x^10 +83*x^9 +89*x^8 -727*x^7 -649*x^6 -593*x^5 -457*x^4 -253*x^3 -197*x^2 -181*x-163) / (x^16 -10*x^8 +1).
Showing 1-3 of 3 results.

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