OFFSET
0,2
LINKS
Colin Barker, Table of n, a(n) for n = 0..832
Vladimir Pletser, Recurrent Relations for Multiple of Triangular Numbers being Triangular Numbers, arXiv:2101.00998 [math.NT], 2021.
Vladimir Pletser, Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations, arXiv:2102.13494 [math.NT], 2021.
Vladimir Pletser, Using Pell equation solutions to find all triangular numbers multiple of other triangular numbers, 2022.
Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).
FORMULA
Let b(n) be A077398(n) then a(n) = b(n)*(b(n)+1)/2.
G.f.: -3*x*(x^2+4*x+1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)). - Colin Barker, Jul 02 2013
Comment from _Vladimir Pletser, Feb 21 2021: (Start)
a(n) = 254 a(n - 2) - a (n - 4) + 18.
a(n) = a(n - 1) + 254 (a(n - 2) - a(n - 3)) - (a (n - 4) - a(n - 5)). (End)
MAPLE
f := gfun:-rectoproc({a(-2) = 3, a(-1) = 0, a(0) = 0, a(1) = 3, a(n) = 254*a(n-2)-a(n-4)+18}, a(n), remember); map(f, [`$`(0 .. 1000)])[] #Vladimir Pletser, Feb 21 2021
MATHEMATICA
Select[Accumulate[Range[0, 5700000]], IntegerQ[(Sqrt[56#+1]-1)/2]&] (* Harvey P. Dale, Jan 18 2013 *)
LinearRecurrence[{1, 254, -254, -1, 1}, {0, 3, 15, 780, 3828}, 30] (* G. C. Greubel, Jan 18 2018 *)
PROG
(PARI) concat(0, Vec(-3*x*(x^2+4*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^100))) \\ Colin Barker, May 15 2015
(Magma) Q:=Rationals(); R<x>:=PowerSeriesRing(Q, 30); [0] cat Coefficients(R!(-3*x*(x^2+4*x+1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)))); // G. C. Greubel, Jan 18 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Bruce Corrigan (scentman(AT)myfamily.com), Nov 05 2002
STATUS
approved