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A082870 Tribonacci array.

%I A082870 #18 Nov 27 2016 22:10:32
%S A082870 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,
%T A082870 8,28,50,45,16,1,1,9,36,77,90,51,10,1,10,45,112,161,126,45,4,1,11,55,
%U A082870 156,266,266,141,30,1,1,12,66,210,414,504,357,126,15,1,13,78,275,615,882
%N A082870 Tribonacci array.
%C A082870 Row sums are tribonacci numbers.
%C A082870 From _Gary W. Adamson_, Nov 15 2016: (Start)
%C A082870 With an alternative format:
%C A082870 1, 0, 0, 0, 0, 0, 0, ...
%C A082870 1, 1, 1, 0, 0, 0, 0, ...
%C A082870 1, 2, 3, 2, 1, 0, 0, ...
%C A082870 1, 3, 6, 7, 6, 3, 1, ...
%C A082870 ... (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)
%D A082870 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".
%H A082870 Reinhard Zumkeller, <a href="/A082870/b082870.txt">Rows n = 0..150 of triangle, flattened</a>
%F A082870 G.f.: x/(1 - x - x^2*y - x^3*y^2). - _Vladeta Jovovic_, May 30 2003
%e A082870 Triangle begins:
%e A082870   1,
%e A082870   1,
%e A082870   1,  1,
%e A082870   1,  2,  1,
%e A082870   1,  3,  3,
%e A082870   1,  4,  6,  2,
%e A082870   1,  5, 10,  7,  1,
%e A082870   1,  6, 15, 16,  6,
%o A082870 (Haskell)
%o A082870 a082870 n k = a082870_tabf !! n !! k
%o A082870 a082870_row n = a082870_tabf !! n
%o A082870 a082870_tabf = map (takeWhile (> 0)) a082601_tabl
%o A082870 -- _Reinhard Zumkeller_, Apr 13 2014
%Y A082870 A082601 is a better version. Cf. A000073, A078802.
%Y A082870 Cf. A004396 (row lengths).
%K A082870 nonn,tabf
%O A082870 0,6
%A A082870 _Gary W. Adamson_, May 24 2003
%E A082870 More terms from _Vladeta Jovovic_, May 30 2003