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%I #2 Mar 30 2012 17:34:28
%S 2,3,3,2,14,2,2,25,25,2,2,10,138,10,2,2,22,219,219,22,2,2,56,112,1118,
%T 112,56,2,2,128,256,1801,1801,256,128,2,2,344,690,1034,8982,1034,690,
%U 344,2,2,854,1710,2566,14551,14551,2566,1710,854,2,2,2036,4072,6108
%N Designed symmetrical sequence with 2*3^n row sum and term: row(n)=3^n; f(n,m) = Floor[(m/Prime[n])*row(n)/2].
%C This kind of 2*3^n row sum sequence is an effort to get the Sierpinski carpet scale three
%C level of symmetry into a triangular/ binomial like sequence.
%F row(n)=3^n;
%F f(n,m) = Floor[(m/Prime[n])*row(n)/2].
%e {2},
%e {3, 3},
%e {2, 14, 2},
%e {2, 25, 25, 2},
%e {2, 10, 138, 10, 2},
%e {2, 22, 219, 219, 22, 2},
%e {2, 56, 112, 1118, 112, 56, 2},
%e {2, 128, 256, 1801, 1801, 256, 128, 2},
%e {2, 344, 690, 1034, 8982, 1034, 690, 344, 2},
%e {2, 854, 1710, 2566, 14551, 14551, 2566, 1710, 854, 2},
%e {2, 2036, 4072, 6108, 8144, 77374, 8144, 6108, 4072, 2036, 2}
%t Clear[v, n, row, f]; row[n_] = 3^n;
%t f[n_, m_] = Floor[(m/Prime[n])*row[n]/2]; v[0] = {1}; v[1] = {3/2, 3/2};
%t v[n_] := v[n] = If[Mod[n, 2] == 0, Join[{1}, Table[ f[n, m], {m, 1,Floor[n/2] - 1}], {row[n] - 2*Sum[ f[n,m], {m, 1, Floor[n/2] - 1}] - 2}, Table[ f[n, m], {m, Floor[n/2] - 1,1, -1}], {1}],
%t Join[{1}, Table[ f[n, m], {m, 1, Floor[n/2] - 1}], {row[n]/2 - Sum[ f[n, m], {m, 1, Floor[n/2] - 1}] - 1, row[n]/2 - Sum[ f[n, m], {m, 1, Floor[n/2] - 1}] - 1}, Table[ f[n, m], {m, Floor[n/2] - 1, 1, -1}], {1}]];
%t Table[FullSimplify[Floor[2*v[n]]], {n, 0, 10}];
%t Flatten[%]
%K nonn,uned,tabl
%O 0,1
%A _Roger L. Bagula_, Dec 23 2008
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