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Triangle read by rows: T(n,m) = A000931(m+6) if m <= floor(n/2), A000931(n+6-m) otherwise, for 0 <= m <= n.
4

%I #23 May 16 2024 10:41:28

%S 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,2,2,2,1,1,1,1,2,2,2,2,

%T 1,1,1,1,2,2,3,2,2,1,1,1,1,2,2,3,3,2,2,1,1,1,1,2,2,3,4,3,2,2,1

%N Triangle read by rows: T(n,m) = A000931(m+6) if m <= floor(n/2), A000931(n+6-m) otherwise, for 0 <= m <= n.

%C The Padovan sequence is pushed back to a(-1)=1, so that the triangle is not almost all ones.

%e The triangle begins:

%e 1;

%e 1, 1;

%e 1, 1, 1;,

%e 1, 1, 1, 1;

%e 1, 1, 2, 1, 1;

%e 1, 1, 2, 2, 1, 1;

%e 1, 1, 2, 2, 2, 1, 1;

%e 1, 1, 2, 2, 2, 2, 1, 1;

%e 1, 1, 2, 2, 3, 2, 2, 1, 1;

%e 1, 1, 2, 2, 3, 3, 2, 2, 1, 1;

%e 1, 1, 2, 2, 3, 4, 3, 2, 2, 1, 1;

%e ...

%t a[-1] = 1; a[0] = 1; a[1] = 1; a[n_] := a[n] = a[n - 2] + a[n - 3]; (* Padovan : A000931 *)

%t Table[If[m <= Floor[n/2], a[m], a[n - m]], {n, 0, 10}, {m, 0, n}]

%Y Cf. A000931, A139147.

%K nonn,tabl,less

%O 0,13

%A _Roger L. Bagula_ and _Gary W. Adamson_, May 31 2008

%E Edited by _N. J. A. Sloane_, Feb 28 2009

%E Non-ASCII characters in %t line corrected by _Wouter Meeussen_, Feb 10 2013

%E Definition corrected and offset changed by _Georg Fischer_, May 16 2024