OFFSET
0,6
COMMENTS
Row sums are tribonacci numbers.
From Gary W. Adamson, Nov 15 2016: (Start)
With an alternative format:
1, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 0, 0, 0, 0, ...
1, 2, 3, 2, 1, 0, 0, ...
1, 3, 6, 7, 6, 3, 1, ...
... (where the k-th row is (1 + x + x^2)^k), let q(x) = (r(x) * r(x^3) * r(x^9) * r(x^27) * ...). Then q(x) is the binomial sequence beginning (1, k, ...). Example: (1, 3, 6, 10, ...) = q(x) with r(x) = (1, 3, 6, 7, 3, 1, 0, 0, 0). (End)
REFERENCES
Thomas Koshy, <"Fibonacci and Lucas Numbers with Applications">, Wiley, 2001; Chapter 47: Tribonacci Polynomials: ("In 1973, V.E. Hoggat, Jr. and M. Bicknell generalized Fibonacci polynomials to Tribonacci polynomials tx(x)"); Table 47.1, page 534: "Tribonacci Array".
LINKS
Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened
FORMULA
G.f.: x/(1 - x - x^2*y - x^3*y^2). - Vladeta Jovovic, May 30 2003
EXAMPLE
Triangle begins:
1,
1,
1, 1,
1, 2, 1,
1, 3, 3,
1, 4, 6, 2,
1, 5, 10, 7, 1,
1, 6, 15, 16, 6,
PROG
(Haskell)
a082870 n k = a082870_tabf !! n !! k
a082870_row n = a082870_tabf !! n
a082870_tabf = map (takeWhile (> 0)) a082601_tabl
-- Reinhard Zumkeller, Apr 13 2014
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gary W. Adamson, May 24 2003
EXTENSIONS
More terms from Vladeta Jovovic, May 30 2003
STATUS
approved