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A000012 * A135839 as infinite lower triangular matrices.
3

%I #14 Mar 27 2022 22:26:32

%S 1,2,1,3,1,1,4,2,1,1,5,2,2,1,1,6,3,2,2,1,1,7,3,3,2,2,1,1,8,4,3,3,2,2,

%T 1,1,9,4,4,3,3,2,2,1,1,10,5,4,4,3,3,2,2,1,1,11,5,5,4,4,3,3,2,2,1,1,12,

%U 6,5,5,4,4,3,3,2,2,1,1,13,6,6,5,5,4,4,3,3,2,2,1,1

%N A000012 * A135839 as infinite lower triangular matrices.

%C Row sums = A024206: (1, 3, 5, 8, 11, 15, 19, ...).

%H G. C. Greubel, <a href="/A135841/b135841.txt">Table of n, a(n) for n = 1..1275</a>

%F T(1, 1) = 1, T(n, 1) = n, T(n, n) = 1, T(n, k) = floor((n - k + 2)/2). - _G. C. Greubel_, Dec 06 2016

%e First few rows of the triangle:

%e 1;

%e 2, 1;

%e 3, 1, 1;

%e 4, 2, 1, 1;

%e 5, 2, 2, 1, 1;

%e 6, 3, 2, 2, 1, 1;

%e 7, 3, 3, 2, 2, 1, 1;

%e ...

%t T[1, 1] := 1; T[n_, 1] := n; T[n_, n_] := 1; T[n_, k_] := Floor[(n - k + 2)/2]; Table[T[n, k], {n, 1, 15}, {k, 1, n}]//Flatten (* _G. C. Greubel_, Dec 06 2016 *)

%Y Cf. A135839, A024206.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Dec 01 2007

%E Terms a(56) and beyond from _G. C. Greubel_, Dec 06 2016