OFFSET
0,1
COMMENTS
"If n is a triangular number, then so are 9*n+1, 25*n+3 and 49*n+6. (Euler, 1775)." Burton, p. 17.
REFERENCES
D. M. Burton, Elementary Number Theory, Allyn and Bacon, Inc. Boston, MA, 1976, p. 17.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=6, a(1)=55, a(2)=153. - Harvey P. Dale, Apr 11 2012
From Elmo R. Oliveira, Oct 23 2024: (Start)
G.f.: (6 + 37*x + 6*x^2)/(1 - x)^3.
E.g.f.: (6 + 49*x + 49*x^2/2)*exp(x).
MATHEMATICA
49*Accumulate[Range[0, 40]]+6 (* or *) LinearRecurrence[{3, -3, 1}, {6, 55, 153}, 40] (* Harvey P. Dale, Apr 11 2012 *)
PROG
(PARI) v=[]; for(n=0, 100, v=concat(v, 49*(n*(n+1)/2)+6)); v
(PARI) for (n=0, 1000, write("b061792.txt", n, " ", 49*n*(n + 1)/2 + 6)) \\ Harry J. Smith, Jul 28 2009
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jason Earls, Jun 22 2001
STATUS
approved