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.

A323848 Irregular triangle read by rows: T(n,d) (n >= 1, d <= n-1 for n>1) = number of n X n integer-valued matrices M such that M_{1,1}=0, M_{n,n}=d, M_{(i+1),j} = M_{i,j} + (0 or 1), M_{i,(j+1)} = M_{i,j} + (0 or 1), and M_{(i+1),(j+1)} = M_{i,j} + (0 or 1).

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%I A323848 #30 Feb 10 2019 08:46:25
%S A323848 0,4,18,25,68,386,256,250,4657,12200,4356,922,54219,432842,608993,
%T A323848 123904,3430,642815,14697256,60650883,49489706,5909761,12868,7852836,
%U A323848 514608568,5713126349,13458882036,6648891794,473497600,48618,98755951,18971384148,558848240787,3406380649146,4857082197177,1489334202216,63799687396
%N A323848 Irregular triangle read by rows: T(n,d) (n >= 1, d <= n-1 for n>1) = number of n X n integer-valued matrices M such that M_{1,1}=0, M_{n,n}=d, M_{(i+1),j} = M_{i,j} + (0 or 1), M_{i,(j+1)} = M_{i,j} + (0 or 1), and M_{(i+1),(j+1)} = M_{i,j} + (0 or 1).
%C A323848 T(n,n-1) = A005157(n-1)^2 for n >= 2. See Knuth (2019) link.
%D A323848 D. E. Knuth, Email to N. J. A. Sloane, Feb 06 2019.
%H A323848 Alois P. Heinz, <a href="/A323848/b323848.txt">Rows n = 1..14, flattened</a>
%H A323848 Don Knuth, <a href="https://cs.stanford.edu/~knuth/papers/noncr-conj.pdf">A conjecture about noncrossing paths</a>, Feb 06 2019.
%F A323848 T(n,1) = binomial(2n,n) - 2.
%e A323848 Triangle begins:
%e A323848   n\d    1      2        3        4        5       6  7
%e A323848    1     0      0        0        0        0       0  0
%e A323848    2     4      0        0        0        0       0  0
%e A323848    3    18     25        0        0        0       0  0
%e A323848    4    68    386      256        0        0       0  0
%e A323848    5   250   4657    12200     4356        0       0  0
%e A323848    6   922  54219   432842   608993   123904       0  0
%e A323848    7  3430 642815 14697256 60650883 49489706 5909761  0
%e A323848 ...
%Y A323848 Columns d=1-2 give: A115112, A306322.
%Y A323848 Cf. A005157, A323849.
%K A323848 nonn,tabf
%O A323848 1,2
%A A323848 _N. J. A. Sloane_, Feb 07 2019
%E A323848 More terms from _Alois P. Heinz_, Feb 07 2019