cp's OEIS Frontend

A211980 Triangle read by rows: T(n,k) = total number of regions in the last n-k+1 shells of n.

%I A211980 #16 Mar 11 2014 01:34:20
%S A211980 1,2,1,3,2,1,5,4,3,2,7,6,5,4,2,11,10,9,8,6,4,15,14,13,12,10,8,4,22,21,
%T A211980 20,19,17,15,11,7,30,29,28,27,25,23,19,15,8,42,41,40,39,37,35,31,27,
%U A211980 20,12,56,55,54,53,51,49,45,41,34,26,14,77,76,75
%N A211980 Triangle read by rows: T(n,k) = total number of regions in the last n-k+1 shells of n.
%C A211980 The set of partitions of n contains n shells and A000041(n) regions. For the definition of "last section of n" see A135010. For the definition of "region of n" see A206437.
%H A211980 Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%F A211980 T(n,1) = A000041(n).
%F A211980 T(n,k) = A000041(n) - A000041(k-1), 1<k<=n.
%F A211980 T(n,k) = Sum_{j=k..n} A187219(j).
%e A211980 Triangle begins:
%e A211980 1;
%e A211980 2,   1;
%e A211980 3,   2,  1;
%e A211980 5,   4,  3,  2;
%e A211980 7,   6,  5,  4,  2;
%e A211980 11, 10,  9,  8,  6,  4;
%e A211980 15, 14, 13, 12, 10,  8,  4;
%e A211980 22, 21, 20, 19, 17, 15, 11,  7;
%e A211980 30, 29, 28, 27, 25, 23, 19, 15,  8;
%e A211980 42, 41, 40, 39, 37, 35, 31, 27, 20, 12;
%e A211980 56, 55, 54, 53, 51, 49, 45, 41, 34, 26, 14;
%e A211980 77, 76, 75, 74, 72, 70, 66, 62, 55, 47, 35, 21;
%Y A211980 Mirror of triangle A211990. Column 1 is A000041, n >= 1. Right border is A187219.
%Y A211980 Cf. A135010, A138121, A182703, A186114, A206437, A212000, A212001.
%K A211980 nonn,tabl
%O A211980 1,2
%A A211980 _Omar E. Pol_, Apr 27 2012