A261932
The first of two consecutive positive integers the sum of the squares of which is equal to the sum of the squares of ten consecutive positive integers.
Original entry on oeis.org
26, 48, 68, 126, 468, 866, 1226, 2268, 8406, 15548, 22008, 40706, 150848, 279006, 394926, 730448, 2706866, 5006568, 7086668, 13107366, 48572748, 89839226, 127165106, 235202148, 871602606, 1612099508, 2281885248, 4220531306, 15640274168, 28927951926
Offset: 1
26 is in the sequence because 26^2 + 27^2 = 7^2 + 8^2 + ... + 16^2.
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,18,-18,0,0,-1,1).
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CoefficientList[Series[2 (4 x^8 - x^7 + x^5 - 63 x^4 + 29 x^3 + 10 x^2 + 11 x + 13)/((1 - x) (x^4 - 4 x^2 - 1) (x^4 + 4 x^2 - 1)), {x, 0, 45}], x] (* Vincenzo Librandi, Sep 07 2015 *)
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Vec(-2*x*(4*x^8-x^7+x^5-63*x^4+29*x^3+10*x^2+11*x+13)/((x-1)*(x^4-4*x^2-1)*(x^4+4*x^2-1)) + O(x^40))
A261933
The first of two consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seventeen consecutive positive integers.
Original entry on oeis.org
40, 91, 2743, 6364, 192004, 445423, 13437571, 31173280, 940438000, 2181684211, 65817222463, 152686721524, 4606265134444, 10685888822503, 322372742188651, 747859530853720, 22561485688071160, 52339481270937931, 1578981625422792583, 3663015829434801484
Offset: 1
40 is in the sequence because 40^2 + 41^2 = 5^2 + 6^2 + ... + 21^2.
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LinearRecurrence[{1,70,-70,-1,1},{40,91,2743,6364,192004},20] (* Harvey P. Dale, Oct 17 2015 *)
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Vec(-x*(40*x^4+51*x^3-148*x^2+51*x+40)/((x-1)*(x^4-70*x^2+1)) + O(x^40))
A261934
The first of ten consecutive positive integers the sum of the squares of which is equal to the sum of the squares of two consecutive positive integers.
Original entry on oeis.org
7, 17, 26, 52, 205, 383, 544, 1010, 3755, 6949, 9838, 18200, 67457, 124771, 176612, 326662, 1210543, 2239001, 3169250, 5861788, 21722389, 40177319, 56869960, 105185594, 389792531, 720952813, 1020490102, 1887478976, 6994543241, 12936973387, 18311951948
Offset: 1
7 is in the sequence because 7^2 + 8^2 + ... + 16^2 = 26^2 + 27^2.
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,18,-18,0,0,-1,1).
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LinearRecurrence[{1,0,0,18,-18,0,0,-1,1},{7,17,26,52,205,383,544,1010,3755},40] (* Harvey P. Dale, Mar 29 2018 *)
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Vec(x*(2*x^8+2*x^7+x^6+2*x^5-27*x^4-26*x^3-9*x^2-10*x-7)/((x-1)*(x^4-4*x^2-1)*(x^4+4*x^2-1)) + O(x^40))
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