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 A262142 The first of ten consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers. 2
 171, 6660, 253071, 9610200, 364934691, 13857908220, 526235577831, 19983094049520, 758831338304091, 28815607761506100, 1094234263598927871, 41552086408997753160, 1577885049278315692371, 59918079786166998557100, 2275309146825067629477591 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For the first of the corresponding nine consecutive positive integers, see A262141. LINKS Colin Barker, Table of n, a(n) for n = 1..632 Index entries for linear recurrences with constant coefficients, signature (39,-39,1). FORMULA a(n) = 39*a(n-1)-39*a(n-2)+a(n-3) for n>3. G.f.: 9*x*(x-19) / ((x-1)*(x^2-38*x+1)). a(n) = 3*(-6-(-3+sqrt(10))*(19+6*sqrt(10))^(-n)+(3+sqrt(10))*(19+6*sqrt(10))^n)/4. - Colin Barker, Mar 03 2016 EXAMPLE 171 is in the sequence because 171^2 + ... + 180^2 = 308085 = 181^2 + ... + 189^2. MATHEMATICA LinearRecurrence[{39, -39, 1}, {171, 6660, 253071}, 30] (* Harvey P. Dale, Sep 26 2015 *) PROG (PARI) Vec(9*x*(x-19)/((x-1)*(x^2-38*x+1)) + O(x^30)) CROSSREFS Cf. A262141. Sequence in context: A332418 A152926 A239270 * A206595 A127959 A046166 Adjacent sequences: A262139 A262140 A262141 * A262143 A262144 A262145 KEYWORD nonn,easy AUTHOR Colin Barker, Sep 12 2015 STATUS approved

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Last modified June 25 13:13 EDT 2024. Contains 373705 sequences. (Running on oeis4.)