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A262062
The first of six consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers.
2
85, 2269, 58969, 1530985, 39746701, 1031883301, 26789219185, 695487815569, 18055893985669, 468757755811885, 12169645757123401, 315942031929396601, 8202323184407188285, 212944460762657498869, 5528353656644687782369, 143524250611999224842785
OFFSET
1,1
COMMENTS
For the first of the corresponding seven consecutive positive integers, see A262063.
FORMULA
a(n) = 27*a(n-1)-27*a(n-2)+a(n-3) for n>3.
G.f.: -x*(x^2-26*x+85) / ((x-1)*(x^2-26*x+1)).
EXAMPLE
85 is in the sequence because 85^2 + ... + 90^2 = 45955 = 78^2 + ... + 84^2.
MATHEMATICA
CoefficientList[Series[(x^2 - 26 x + 85)/((1 - x) (x^2 - 26 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Sep 10 2015 *)
PROG
(PARI) Vec(-x*(x^2-26*x+85)/((x-1)*(x^2-26*x+1)) + O(x^20))
(Magma) I:=[85, 2269, 58969]; [n le 3 select I[n] else 27*Self(n-1)-27*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Sep 10 2015
CROSSREFS
Cf. A262063.
Sequence in context: A020310 A163692 A221339 * A220736 A157110 A076463
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Sep 09 2015
STATUS
approved