A261932 The first of two consecutive positive integers the sum of the squares of which is equal to the sum of the squares of ten consecutive positive integers.

26, 48, 68, 126, 468, 866, 1226, 2268, 8406, 15548, 22008, 40706, 150848, 279006, 394926, 730448, 2706866, 5006568, 7086668, 13107366, 48572748, 89839226, 127165106, 235202148, 871602606, 1612099508, 2281885248, 4220531306, 15640274168, 28927951926

Offset

1,1

Comments

For the first of the corresponding ten consecutive positive integers, see A261934.

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.: -2*x*(4*x^8-x^7+x^5-63*x^4+29*x^3+10*x^2+11*x+13) / ((x-1)*(x^4-4*x^2-1)*(x^4+4*x^2-1)).

a(n) = a(n-1) + 18*a(n-4) - 18*a(n-5) - a(n-8) + a(n-9) for n>8. - Vincenzo Librandi, Sep 07 2015

Example

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

Mathematica

CoefficientList[Series[2 (4 x^8 - x^7 + x^5 - 63 x^4 + 29 x^3 + 10 x^2 + 11 x + 13)/((1 - x) (x^4 - 4 x^2 - 1) (x^4 + 4 x^2 - 1)), {x, 0, 45}], x] (* Vincenzo Librandi, Sep 07 2015 *)

Prog

(PARI) Vec(-2*x*(4*x^8-x^7+x^5-63*x^4+29*x^3+10*x^2+11*x+13)/((x-1)*(x^4-4*x^2-1)*(x^4+4*x^2-1)) + O(x^40))

Crossrefs

Cf. A001652, A031138, A261933, A261934, A261935.

Sequence in context: A159651 A118367 A316120 * A364025 A324041 A375139

Adjacent sequences: A261929 A261930 A261931 * A261933 A261934 A261935

Keyword

nonn,easy

Author

Colin Barker, Sep 06 2015

Status

approved