A262139 The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.
22, 145, 862, 5041, 29398, 171361, 998782, 5821345, 33929302, 197754481, 1152597598, 6717831121, 39154389142, 228208503745, 1330096633342, 7752371296321, 45184131144598, 263352415571281, 1534930362283102, 8946229758127345, 52142448186480982
Offset: 1
Examples
22 is in the sequence because 22^2 + ... + 29^2 = 5244 = 20^2 + ... + 28^2.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
Crossrefs
Cf. A262140.
Programs
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Mathematica
LinearRecurrence[{7,-7,1},{22,145,862},30] (* Harvey P. Dale, Apr 19 2016 *) -
PARI
Vec(-x*(x^2-9*x+22)/((x-1)*(x^2-6*x+1)) + O(x^40))
Formula
a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.
G.f.: -x*(x^2-9*x+22) / ((x-1)*(x^2-6*x+1)).
a(n) = (-14+3*(3-2*sqrt(2))^(1+n)+3*(3+2*sqrt(2))^(1+n))/4. - Colin Barker, Mar 05 2016
Comments