A262140 The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eight consecutive positive integers.
20, 136, 812, 4752, 27716, 161560, 941660, 5488416, 31988852, 186444712, 1086679436, 6333631920, 36915112100, 215157040696, 1254027132092, 7309005751872, 42600007379156, 248291038523080, 1447146223759340, 8434586304032976, 49160371600438532
Offset: 1
Examples
20 is in the sequence because 20^2 + ... + 28^2 = 5244 = 22^2 + ... + 29^2.
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-7,1).
Programs
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PARI
Vec(4*x*(x-5)/((x-1)*(x^2-6*x+1)) + O(x^40))
Formula
a(n) = 4*A076708(n+1).
a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.
G.f.: 4*x*(x-5) / ((x-1)*(x^2-6*x+1)).
E.g.f.: exp(x)*(exp(2*x)*(4*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)) - 4). - Stefano Spezia, Aug 08 2025
Comments