|
%I #2 Mar 30 2012 17:25:11
%S 1,7,2,12,5,1,26,15,7,2,35,22,12,5,1,57,40,26,15,7,2,70,51,35,22,12,5,
%T 1,100,77,57,40,26,15,7,2
%N Pentagonal wave sequence triangle.
%C Row sums = A086500: 1, 9, 18, 50, 75, 147, 196...
%F Odd columns are terms of A104584, pentagonal wave sequence of the first kind, (starting with 1): 1, 7, 12, 26, 35, 57, 70... Even columns are terms of A104585, pentagonal wave sequence of the second kind (starting with 2): 2, 5, 15, 22, 40, 51... Odd rows are pentagonal numbers (A000326) starting with "1" at the right. Even rows are second pentagonal numbers (A005449) starting with 2 at the right. The triangle is extracted from a matrix product A * B, A = [1; 1, 2; 1, 2, 1; 1, 2, 1, 2;...], B = [1; 3, 1; 5, 3, 1; 7, 5, 3, 1;...] (both infinite lower triangular matrices, with the rest zeros).
%e The first few rows are:
%e 1;
%e 7, 2;
%e 12, 5, 1;
%e 26, 15, 7, 2;
%e 35, 22, 12, 5, 1;
%e 57, 40, 26, 15, 7, 2;
%e 70, 51, 35, 22, 12, 5, 1;
%e ...
%Y Cf. A086500, A104584, A104585, A000326, A005449, A049452, A033570, A049453, A033568.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Mar 17 2005
|
