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%I #35 May 06 2022 20:27:22
%S 0,15,105,4950,33930,1594005,10925475,513264780,3517969140,
%T 165269665275,1132775137725,53216318953890,364750076378430,
%U 17135489433487425,117448391818716855,5517574381263997080,37818017415550449000,1776641815277573572455,12177284159415425861265
%N Triangular numbers that are 5 times another triangular number.
%C The triangular numbers that are 1/5 are in A077260.
%H Colin Barker, <a href="/A077261/b077261.txt">Table of n, a(n) for n = 0..797</a>
%H Vladimir Pletser, <a href="https://arxiv.org/abs/2101.00998">Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers</a>, arXiv:2101.00998 [math.NT], 2021.
%H Vladimir Pletser, <a href="https://arxiv.org/abs/2102.13494">Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations</a>, arXiv:2102.13494 [math.NT], 2021.
%H Vladimir Pletser, <a href="https://www.researchgate.net/profile/Vladimir-Pletser/publication/359808848_USING_PELL_EQUATION_SOLUTIONS_TO_FIND_ALL_TRIANGULAR_NUMBERS_MULTIPLE_OF_OTHER_TRIANGULAR_NUMBERS/">Using Pell equation solutions to find all triangular numbers multiple of other triangular numbers</a>, 2022.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,322,-322,-1,1).
%F a(n) = 5*A077260(n).
%F G.f.: (-15*x*(x^2+6*x+1))/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
%F a(n) = 322*a(n-2) - a(n-4) + 120. - _Vladimir Pletser_, Feb 09 2021
%e a(3)=5*990=4950.
%t CoefficientList[Series[(-15 x (x^2 + 6 x + 1))/((x - 1) (x^2 - 18 x + 1) (x^2 + 18 x + 1)), {x, 0, 18}], x] (* _Michael De Vlieger_, Apr 21 2021 *)
%Y Subsequence of A000217.
%Y Cf. A077259, A077260, A077262.
%K easy,nonn
%O 0,2
%A Bruce Corrigan (scentman(AT)myfamily.com), Nov 01 2002
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