A082870 Tribonacci array.

1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 4, 6, 2, 1, 5, 10, 7, 1, 1, 6, 15, 16, 6, 1, 7, 21, 30, 19, 3, 1, 8, 28, 50, 45, 16, 1, 1, 9, 36, 77, 90, 51, 10, 1, 10, 45, 112, 161, 126, 45, 4, 1, 11, 55, 156, 266, 266, 141, 30, 1, 1, 12, 66, 210, 414, 504, 357, 126, 15, 1, 13, 78, 275, 615, 882

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

A082601 is a better version. Cf. A000073, A078802.

Cf. A004396 (row lengths).

Sequence in context: A124054 A299208 A334187 * A026009 A137171 A010356

Adjacent sequences: A082867 A082868 A082869 * A082871 A082872 A082873

Keyword

nonn,tabf

Author

Gary W. Adamson, May 24 2003

Extensions

More terms from Vladeta Jovovic, May 30 2003

Status

approved