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Triangle T(h, w) = number of rotes of height h and wayage w.
1

%I #7 Nov 23 2013 23:50:53

%S 1,1,3,4,77

%N Triangle T(h, w) = number of rotes of height h and wayage w.

%C T(h, w) = |{positive integers m : A109301(m) = h and A001221(m) = w}|.

%C Let c(h) = 1 for h = 0 and A050924(h) for h > 0. In other words, c(h) is the sequence [1, A050924] = [1,1,2,9,10^9, ...] that begins with 1 and continues with the terms of A050924. Then the number of nonzero entries in row h is c(h) and their sum is A109300(h). See A111798 for definitions and further details.

%H J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>

%e Table T(h, w), omitting zeros, begins as follows:

%e h\w| 0 ` 1 ` 2 ` 3 ` 4 ` 5 ` 6 ` 7 ` 8 ` 9

%e ---+---------------------------------------

%e `0 | 1

%e `1 | ` ` 1

%e `2 | ` ` 3 ` 4

%e `3 | ` `77 ` ? ` ? ` ? ` ? ` ? ` ? ` ? ` ?

%Y Cf. A001221, A007097, A050924, A061396, A062504, A062537, A062860.

%Y Cf. A109300, A109301, A111791, A111792, A111793, A111798, A111800.

%K nonn,tabf

%O 1,3

%A _Jon Awbrey_, Sep 01 2005 - Sep 02 2005