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A122542
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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.
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11
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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, 66, 88, 50, 12, 1, 0, 2, 24, 102, 192, 170, 72, 14, 1, 0, 2, 28, 146, 360, 450, 292, 98, 16, 1, 0, 2, 32, 198, 608, 1002, 912, 462, 128, 18, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Riordan array (1, x*(1+x)/(1-x)) . Rising and falling diagonals are the tribonacci numbers A000213, A001590.
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FORMULA
| Sum_{k, 0<=k<=n}x^k*T(n,k) = A000007(n), A001333(n), A104934(n), A122558(n), A122690(n), A091928(n) for x = 0, 1, 2, 3, 4, 5 . DELEHAM Philippe, Jan 25 2012 .
Sum_{k, 0<=k<=n}3^(n-k)*T(n,k) = A086901(n).
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
T(2*n,n)=A123164(n).
T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1), n>1. - DELEHAM Philippe, Jan 25 2012
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EXAMPLE
| Triangle begins:
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, 66, 88, 50, 12, 1;
0, 2, 24, 102, 192, 170, 72, 14, 1;
0, 2, 28, 146, 360, 450, 292, 98, 16, 1;
0, 2, 32, 198, 608, 1002, 912, 462, 128, 18, 1;
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CROSSREFS
| Cf. A113413, A035607. Diagonals : A000012, A005843, A001105, A035597-A035606. Columns : A000007, A040000, A008575, A005899, A008412-A008416, A008418, A008420, A035706-A035745.
Sequence in context: A206022 A115247 A204163 * A098542 A141343 A066709
Adjacent sequences: A122539 A122540 A122541 * A122543 A122544 A122545
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2006, May 28 2007
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