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A082870 Tribonacci array. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A215064 A124054 A299208 * 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

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Last modified February 21 23:29 EST 2019. Contains 320381 sequences. (Running on oeis4.)