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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.
4
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
1,1
COMMENTS
For the first of the corresponding ten consecutive positive integers, see A261934.
FORMULA
G.f.: -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)).
a(n) = a(n-1) + 18*a(n-4) - 18*a(n-5) - a(n-8) + a(n-9) for n>8. - Vincenzo Librandi, Sep 07 2015
EXAMPLE
26 is in the sequence because 26^2 + 27^2 = 7^2 + 8^2 + ... + 16^2.
MATHEMATICA
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 *)
PROG
(PARI) 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))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 06 2015
STATUS
approved