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Array T(n,k) of k-th order Fibonacci numbers read by antidiagonals in up-direction.
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%I #10 May 07 2013 09:57:16

%S 2,3,3,4,5,5,5,7,9,8,6,9,13,17,13,7,11,17,25,31,21,8,13,21,33,49,57,

%T 34,9,15,25,41,65,94,105,55,10,17,29,49,81,129,181,193,89,11,19,33,57,

%U 97,161,253,349,355,144,12,21,37,65,113,193,321,497,673,653,233

%N Array T(n,k) of k-th order Fibonacci numbers read by antidiagonals in up-direction.

%D N. Wirth, Algorithmen und Datenstrukturen, 1975, table 2.15 (ch. 2.3.4)

%H T. D. Noe, <a href="/A061451/b061451.txt">Rows n=1..50 of triangle, flattened</a>

%e 2, 3, 5, 8 ... first order, a(1)=2, a(3)=3, a(6)=5, a(10)=8, ...

%e 3, 5, 9,17 ... 2nd order, a(2)=3, a(5)=5, a(9)=9, ...

%e 4, 7,13,25 ... 3rd order, a(4)=4, a(8)=7, ...

%e 5, 9,17,33 ... 4th order, a(7)=5, ...

%t max = 12; Clear[f]; f[k_, n_] /; n > k := f[k, n] = Sum[f[k, n - j], {j, 1, k + 1}]; f[k_, n_] = 1; t = Table[ Table[ f[k, n], {n, k + 1, max}], {k, 1, max}]; Table[ t[[k - n + 1, n]], {k, 1, max - 1}, {n, 1, k}] // Flatten (* _Jean-François Alcover_, Apr 10 2013 *)

%Y Rows 1..6: A000045, A000213, A000288, A000322, A000383, A060455.

%K nonn,easy,tabl,nice

%O 1,1

%A _Frank Ellermann_, Jun 11 2001