A257824 -id:A257824 - cp's OEIS frontend

A257823 Positive integers whose square is the sum of 59 consecutive squares.

413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727, 452101247, 587437689, 9744411267, 12661399351, 479226895309, 622683396153, 10329066750171, 13421071367333, 507980056926293, 660043812484491, 10948801010769993, 14226322987973629, 538458381114975271

Offset: 1

Colin Barker, May 10 2015

Positive integers x in the solutions to 2*x^2-118*y^2-6844*y-133458 = 0.

			413 is in the sequence because 413^2 = 170569 = 22^2+23^2+...+80^2.

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).

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

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

LinearRecurrence[{0, 0, 0, 1060, 0, 0, 0, -1}, {413, 531, 8673, 11269, 426511, 554187, 9192849, 11944727}, 30] (* Vincenzo Librandi, May 11 2015 *)

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))

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).

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

Colin Barker, May 10 2015

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

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

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,7398,0,0,0,0,0,-1).

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

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

 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 *)

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))

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)).

cp's OEIS Frontend

A257823 Positive integers whose square is the sum of 59 consecutive squares.

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