OFFSET
1,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
M. Feinberg, Fibonacci-Tribonacci, Fib. Quart. 1(3) (1963), 71-74.
Eric Weisstein's World of Mathematics, Tribonacci Number.
Index entries for linear recurrences with constant coefficients, signature (3, 1, 3, -7, 1, -1, 1).
FORMULA
a(n) = Sum_{i=1..n} A000213(i)^2.
a(n)= 3*a(n-1) +a(n-2) +3*a(n-3) -7*a(n-4) +a(n-5) -a(n-6) +a(n-7). G.f.: (x^3-x^2+3*x-1)*(1+x)^2/((x-1)*(x^3+x^2+3*x-1)*(x^3-x^2-x-1)). - R. J. Mathar, Aug 11 2009
EXAMPLE
a(6) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 + 9^2 = 118.
MATHEMATICA
Accumulate[LinearRecurrence[{1, 1, 1}, {1, 1, 1}, 30]^2] (* Harvey P. Dale, Nov 11 2011 *)
LinearRecurrence[{3, 1, 3, -7, 1, -1, 1}, {1, 2, 3, 12, 37, 118, 407}, 26] (* Ray Chandler, Aug 02 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, May 14 2005
STATUS
approved