cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A341694 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).

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