Search: id:A122542
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%I A122542
%S A122542 1,0,1,0,2,1,0,2,4,1,0,2,8,6,1,0,2,12,18,8,1,0,2,16,38,32,10,1,0,2,20,
%T A122542 66,88,50,12,1,0,2,24,102,192,170,72,14,1,0,2,28,146,360,450,292,98,16,
%U A122542 1,0,2,32,198,608,1002,912,462,128,18,1
%N A122542 Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 2, -1, 0, 0, 0, 
               0, 0, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the 
               oprator defined in A084938.
%C A122542 Riordan array (1, x*(1+x)/(1-x)) . Rising and falling diagonals are the 
               tribonacci numbers A000213, A001590.
%F A122542 Sum_{k, 0<=k<=n}x^k*T(n,k) = A001333(n), A104934(n) for x=1, 2 . Sum_{k, 
               0<=k<=n}3^(n-k)*T(n,k) = A086901(n).
%F A122542 Sum_{k, 0<=k<=n}2^(n-k)*T(n,k)=A007483(n-1), n>=1 . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 08 2006
%F A122542 T(2*n,n)=A123164(n+1).
%e A122542 Triangle begins:
%e A122542 1;
%e A122542 0, 1;
%e A122542 0, 2, 1;
%e A122542 0, 2, 4, 1;
%e A122542 0, 2, 8, 6, 1;
%e A122542 0, 2, 12, 18, 8, 1;
%e A122542 0, 2, 16, 38, 32, 10, 1;
%e A122542 0, 2, 20, 66, 88, 50, 12, 1;
%e A122542 0, 2, 24, 102, 192, 170, 72, 14, 1;
%e A122542 0, 2, 28, 146, 360, 450, 292, 98, 16, 1;
%e A122542 0, 2, 32, 198, 608, 1002, 912, 462, 128, 18, 1;
%Y A122542 Cf. A113413, A035607. Diagonals : A000012, A005843, A001105, A035597-A035606. 
               Columns : A000007, A040000, A008575, A005899, A008412-A008416, A008418, 
               A008420, A035706-A035745.
%Y A122542 Sequence in context: A144106 A104558 A115247 this_sequence A098542 A141343 
               A066709
%Y A122542 Adjacent sequences: A122539 A122540 A122541 this_sequence A122543 A122544 
               A122545
%K A122542 nonn,tabl
%O A122542 0,5
%A A122542 Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2006, May 28 2007

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