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
Examples
25 is in the sequence because 25^2 + 26^2 + 27^2 = 2030 = 21^2 + 22^2 + 23^2 + 24^2.
Links
- Colin Barker, Table of n, a(n) for n = 1..873
- Index entries for linear recurrences with constant coefficients, signature (15,-15,1).
Programs
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Mathematica
LinearRecurrence[{15,-15,1},{25,361,5041},20] (* Harvey P. Dale, Jul 16 2025 *) -
PARI
Vec(-x*(x^2-14*x+25)/((x-1)*(x^2-14*x+1)) + O(x^40))
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
Comments