A261974 The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of three consecutive positive integers.
67, 3307, 152275, 7001563, 321919843, 14801311435, 680538406387, 31289965382587, 1438657869192835, 66146972017488043, 3041322054935257363, 139834667555004350875, 6429353385475264883107, 295610421064307180272267, 13591650015572655027641395
Offset: 1
Examples
67 is in the sequence because 67^2 + ... + 77^2 = 57134 = 137^2 + 138^2 + 139^2.
Links
- Colin Barker, Table of n, a(n) for n = 1..601
- Index entries for linear recurrences with constant coefficients, signature (47,-47,1).
Programs
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Mathematica
LinearRecurrence[{47,-47,1},{67,3307,152275},20] (* Harvey P. Dale, Jul 02 2016 *) -
PARI
Vec(x*(5*x^2-158*x-67)/((x-1)*(x^2-46*x+1)) + O(x^40))
Formula
a(n) = 47*a(n-1)-47*a(n-2)+a(n-3) for n>3.
G.f.: x*(5*x^2-158*x-67) / ((x-1)*(x^2-46*x+1)).
a(n) = -5+3*sqrt(3/11)*(23+4*sqrt(33))^(-n)*(-1+(23+4*sqrt(33))^(2*n)). - Colin Barker, Mar 03 2016
Comments