Search: id:A130754
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%I A130754
%S A130754 1,2,2,2,2,6,2,4,6,2,10,20,2,6,15,20,2,14,42,70,2,8,28,56,70,2,18,72,
%T A130754 168,252,2,10,45,120,210,252,2,22,110,330,660,924,2,12,66,220,495,792,
%U A130754 924,2,26,156,572,1430,2574,3432,2,14,91,364,1001,2002,3003,3432,2,30
%N A130754 A folded back triangular sequence of the binomial / Pascal's triangle 
               A007318: half of the sequence is taken and doubled except for the 
               odd middle terms which remain the same.
%C A130754 This fold back operation leaves the row sums at 2^n.
%F A130754 a(n,i)== If[n > 0 && i == 0, 2, If[Mod[n, 2] == 0, binomial[n, i], 2*binomial[n, 
               i]]];
%e A130754 {1},
%e A130754 {2},
%e A130754 {2, 2},
%e A130754 {2, 6},
%e A130754 {2, 4, 6},
%e A130754 {2, 10, 20},
%e A130754 {2, 6, 15, 20},
%e A130754 {2, 14, 42, 70},
%e A130754 {2, 8, 28, 56, 70},
%e A130754 {2, 18, 72, 168, 252},
%e A130754 {2, 10, 45, 120, 210, 252}
%t A130754 f[n_, i_] = If[n > 0 && i == 0, 2, If[Mod[n, 2] == 0, Binomial[n, i], 
               2*Binomial[n, i]]]; Table[Table[f[n, i], {i, 0, Floor[n/2]}], {n, 
               0, 20}]; Flatten[%]
%Y A130754 Cf. A007318.
%Y A130754 Sequence in context: A073124 A070877 A156717 this_sequence A164126 A163368 
               A151948
%Y A130754 Adjacent sequences: A130751 A130752 A130753 this_sequence A130755 A130756 
               A130757
%K A130754 nonn,tabf
%O A130754 1,2
%A A130754 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jul 13 2007

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