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A186807 Triangle read by rows: T(n,p) (n >= 2, 1 <= p <= n-1) = number of compositions of n into p parts, with first part >= all other parts.

%I A186807 #26 Aug 06 2014 17:30:05
%S A186807 1,1,1,1,2,1,1,3,2,1,1,4,4,3,1,1,5,7,6,3,1,1,6,11,11,8,4,1,1,7,16,19,
%T A186807 17,11,4,1,1,8,22,31,32,26,13,5,1,1,9,29,48,56,54,35,17,5,1,1,10,37,
%U A186807 71,93,102,82,48,20,6,1,1,11,46,101,148,180,172,120,63,24,6,1
%N A186807 Triangle read by rows: T(n,p) (n >= 2, 1 <= p <= n-1) = number of compositions of n into p parts, with first part >= all other parts.
%C A186807 This triangle arose in connection with a problem involving "lunar arithmetic".
%C A186807 Take the triangle formed by the antidiagonals of A156041 and reverse each row.
%H A186807 D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a> [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
%H A186807 <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>
%e A186807 Triangle begins:
%e A186807 1,
%e A186807 1, 1,
%e A186807 1, 2, 1,
%e A186807 1, 3, 2, 1,
%e A186807 1, 4, 4, 3, 1,
%e A186807 1, 5, 7, 6, 3, 1,
%e A186807 1, 6, 11, 11, 8, 4, 1,
%e A186807 1, 7, 16, 19, 17, 11, 4, 1,
%e A186807 1, 8, 22, 31, 32, 26, 13, 5, 1,
%e A186807 1, 9, 29, 48, 56, 54, 35, 17, 5, 1,
%e A186807 ...
%Y A186807 Cf. A156041. This is also A184957 with the last diagonal omitted.
%K A186807 nonn,tabl
%O A186807 2,5
%A A186807 _N. J. A. Sloane_, Feb 26 2011