OFFSET
0,3
COMMENTS
The triangular numbers multiplied by 6 are in A077290.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Vladimir Pletser, Triangular Numbers Multiple of Triangular Numbers and Solutions of Pell Equations, arXiv:2102.13494 [math.NT], 2021.
Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).
FORMULA
Let b(n) be A077288. Then a(n)=b(n)*(b(n)+1)/2.
G.f.: -x*(x^2+5*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)). - Colin Barker, Jul 02 2013
a(n) = 98*a(n-2) - a(n-4) + 7. - Vladimir Pletser, Feb 19 2021
EXAMPLE
b(3)=14 so a(3) = 14*15/2 = 105, etc.
MAPLE
f := gfun:-rectoproc({a(-2) = 1, a(-1) = 0, a(0) = 0, a(1) = 1, a(n) = 98*a(n-2)-a(n-4)+7}, a(n), remember); map(f, [`$`(0 .. 1000)])[]; # Vladimir Pletser, Feb 19 2021
MATHEMATICA
tr6Q[n_]:= IntegerQ[1/2 (Sqrt[1+48n]-1)]; Select[Accumulate[ Range[0, 1380000]], tr6Q] (* Harvey P. Dale, Apr 21 2011 *)
PROG
(PARI)
T(n)=n*(n+1)\2;
istriang(n)=issquare(8*n+1);
for(n=0, 10^10, t=T(n); if ( t%6==0 && istriang(t\6), print1(t\6, ", ") ) );
\\ Joerg Arndt, Jul 03 2013
(PARI) concat(0, Vec(-x*(x^2+5*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))) \\ Colin Barker, May 15 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Bruce Corrigan (scentman(AT)myfamily.com), Nov 03 2002
STATUS
approved