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.

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.

Links

Colin Barker, Table of n, a(n) for n = 1..706

Index entries for linear recurrences with constant coefficients, signature (27,-27,1).

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

Adjacent sequences: A262059 A262060 A262061 * A262063 A262064 A262065

Keyword

nonn,easy

Author

Colin Barker, Sep 09 2015

Status

approved