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A261996
The first of twenty-one consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.
2
8, 44, 128, 788, 2024, 5948, 15176, 87764, 223712, 655316, 1670312, 9654332, 24607376, 72079892, 183720224, 1061889836, 2706588728, 7928133884, 20207555408, 116798228708, 297700153784, 872022648428, 2222647375736, 12846743269124, 32744310328592
OFFSET
1,1
COMMENTS
For the first of the corresponding four consecutive positive integers, see A261995.
FORMULA
G.f.: 4*x*(x^8+3*x^7+3*x^6+9*x^5-89*x^4-165*x^3-21*x^2-9*x-2) / ((x-1)*(x^8-110*x^4+1)).
EXAMPLE
8 is in the sequence because 8^2 + ... + 28^2 = 7574 = 42^2 + ... + 45^2.
PROG
(PARI) Vec(4*x*(x^8+3*x^7+3*x^6+9*x^5-89*x^4-165*x^3-21*x^2-9*x-2)/((x-1)*(x^8-110*x^4+1)) + O(x^40))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 08 2015
STATUS
approved