Search: id:A155123
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%I A155123
%S A155123 1,2,2,2,0,4,4,0,4,8,12,0,8,32,8,48
%V A155123 1,2,2,2,0,4,4,0,-4,8,12,0,8,-32,8,48
%N A155123 Six levels of the coefficient triangle of the Pascal-Sierpinski functions.
%C A155123 Row sums are 2^(n+1);
%C A155123 {1, 2, 4, 8, 16, 32,...}.
%F A155123 Triangle:
%F A155123 {{1},
%F A155123 {1, 1},
%F A155123 {1, 2*n, 1},
%F A155123 {1, f[n], f[n], 1},
%F A155123 {1, g[n], 6 + 24 *(n - 1) + 28*(n - 1)^2 + 8* ( n - 1)^3, g[n], 1},
%F A155123 {1, h[n], k[n - 1] - h[n] - 1, k[n - 1] - h[n] - 1, h[n], 1}}
%F A155123 f[n_]=3*n^2 - (n - 1)^2;
%F A155123 g[n_]=-2 + 2 *n + 2* n^2 + 2 n^3;
%F A155123 h[n_]=-3 + 2 n + 2 n^2 + 2 n^3 + 2*n^4;
%F A155123 k[n_]=16+ 80 n + 140 *n^2 + 100*n^3 + 24* n^4;
%F A155123 These functions and the triangles they make are general Pascal-Sierpinski
%F A155123 functions.
%e A155123 {1},
%e A155123 {2},
%e A155123 {2, 2},
%e A155123 {0, 4, 4},
%e A155123 {0, -4, 8, 12},
%e A155123 {0, 8, -32, 8, 48}
%t A155123 a1 = {{1},
%t A155123 {1, 1},
%t A155123 {1, 2 *n, 1},
%t A155123 {1, -1 + 2 *n + 2 n^2, -1 + 2 n + 2 n^2, 1},
%t A155123 {1, -2 + 2 *n + 2 n^2 + 2 n^3, 2 - 8 n + 4 n^2 + 8 n^3, -2 + 2* n + 2 
               n^2 + 2 n^3, 1},
%t A155123 {1, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, 
               2 + 2 n - 18 n^2 + 2 n^3 + 22 n^4, -3 + 2 n + 2 n^2 + 2 n^3 + 2 n^4, 
               1}}
%t A155123 Table[CoefficientList[Apply[Plus, a1[[m]]], n], {m, 1, Length[a1]}];
%t A155123 Flatten[%]
%Y A155123 A142463
%Y A155123 Sequence in context: A103223 A091399 A000091 this_sequence A125938 A158851 
               A151930
%Y A155123 Adjacent sequences: A155120 A155121 A155122 this_sequence A155124 A155125 
               A155126
%K A155123 tabl,uned,sign
%O A155123 0,2
%A A155123 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 20 2009

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