A261972 The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.

25, 361, 5041, 70225, 978121, 13623481, 189750625, 2642885281, 36810643321, 512706121225, 7141075053841, 99462344632561, 1385331749802025, 19295182152595801, 268747218386539201, 3743165875258953025, 52135575035238803161, 726154884618084291241

Offset

1,1

Comments

For the first of the corresponding four consecutive positive integers, see A157088.

Links

Colin Barker, Table of n, a(n) for n = 1..873

Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

Formula

a(n) = 15*a(n-1)-15*a(n-2)+a(n-3) for n>3.

G.f.: -x*(x^2-14*x+25) / ((x-1)*(x^2-14*x+1)).

a(n) = (-2-(7-4*sqrt(3))^n*(-2+sqrt(3))+(2+sqrt(3))*(7+4*sqrt(3))^n)/2. - Colin Barker, Mar 05 2016

Example

25 is in the sequence because 25^2 + 26^2 + 27^2 = 2030 = 21^2 + 22^2 + 23^2 + 24^2.

Prog

(PARI) Vec(-x*(x^2-14*x+25)/((x-1)*(x^2-14*x+1)) + O(x^40))

Crossrefs

Cf. A157088, A261973, A261974.

Sequence in context: A188487 A306083 A077512 * A197678 A197536 A045622

Adjacent sequences: A261969 A261970 A261971 * A261973 A261974 A261975

Keyword

nonn,easy

Author

Colin Barker, Sep 07 2015

Status

approved