%I #15 Feb 19 2021 19:02:06
%S 1,1,1,2,1,1,2,2,2,1,1,1,2,3,1,1,1,3,2,5,1,3,2,1,4,2,8,1,3,3,3,3,7,2,
%T 13,1,1,1,3,5,5,11,2,21,1,1,2,4,3,8,9,18,2,34,1,2,1,1,5,3,13,17,29,2,
%U 55,1,2,1,1,4,9,3,21,31,47,2,89,1
%N Square array T(n, k) read by antidiagonals upwards, n, k > 0: T(n, k) = A227736(n, k) for k = 1..A005811(n), and T(n, k) = T(n, k - A005811(n)) + ... + T(n, k-1) for k > A005811(n).
%C This table contains all Fibonacci sequences of order m > 0 with positive terms:
%C - order 1 corresponds to constant sequences (n in A126646),
%C - order 2 corresponds to Fibonacci-like sequences (n in A043569),
%C - order 3 corresponds to tribonacci-like sequences (n in A043570),
%C - order 4 corresponds to tetranacci-like sequences (n in A043571).
%C For any n > 0, the row A341746(n) corresponds to the n-th row from which the first term has been removed.
%H Rémy Sigrist, <a href="/A341694/b341694.txt">Table of n, a(n) for n = 1..11325</a>
%H Rémy Sigrist, <a href="/A341694/a341694.png">Colored representation of the table for n, k = 1..1024</a>
%H Rémy Sigrist, <a href="/A341694/a341694.gp.txt">PARI program for A341694</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Generalizations_of_Fibonacci_numbers#Fibonacci_numbers_of_higher_order">Fibonacci numbers of higher order</a>
%H <a href="/index/Fi#Fibonacci">Index entries for sequences related to Fibonacci numbers</a>
%F T(A341746(n), k) = T(n, k+1).
%F T(n, 1) = A136480(n).
%e Array T(n, k) begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e ---+---------------------------------------------------------
%e 1| 1 1 1 1 1 1 1 1 1 1 1 1 1 1 --> A000012
%e 2| 1 1 2 3 5 8 13 21 34 55 89 144 233 377 --> A000045
%e 3| 2 2 2 2 2 2 2 2 2 2 2 2 2 2 --> A007395
%e 4| 2 1 3 4 7 11 18 29 47 76 123 199 322 521 --> A000032
%e 5| 1 1 1 3 5 9 17 31 57 105 193 355 653 1201 --> A000213
%e 6| 1 2 3 5 8 13 21 34 55 89 144 233 377 610 --> A000045
%e 7| 3 3 3 3 3 3 3 3 3 3 3 3 3 3 --> A010701
%e 8| 3 1 4 5 9 14 23 37 60 97 157 254 411 665 --> A104449
%e 9| 1 2 1 4 7 12 23 42 77 142 261 480 883 1624 --> A275778
%e 10| 1 1 1 1 4 7 13 25 49 94 181 349 673 1297 --> A000288
%o (PARI) See Links section.
%Y Cf. A005811, A043569, A043570, A043571, A126646, A136480, A227736, A341699, A341746.
%Y Cf. A000012, A000032, A000045, A000213, A000288, A007395, A010701, A104449, A275778.
%K nonn,tabl,base
%O 1,4
%A _Rémy Sigrist_, Feb 17 2021