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

Author

Colin Barker, Sep 06 2015

Keywords

• nonn
• easy

Comments

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

Examples

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

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).

Crossrefs

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

Programs

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 *)

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))

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)).