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.

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

1,1

Comments

For the first of the corresponding two consecutive positive integers, see A261932.

Links

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).

Formula

G.f.: 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)).

Example

7 is in the sequence because 7^2 + 8^2 + ... + 16^2 = 26^2 + 27^2.

Mathematica

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 *)

Prog

(PARI) 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))

Crossrefs

Cf. A001652, A031138, A261932, A261933, A261935.

Sequence in context: A300186 A355680 A354672 * A253075 A011537 A283610

Adjacent sequences: A261931 A261932 A261933 * A261935 A261936 A261937

Keyword

nonn,easy

Author

Colin Barker, Sep 06 2015

Status

approved