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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
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
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.)