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A152815
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Triangle T(n,k), read by rows given by [1,0,-1,0,0,0,0,0,0,...] DELTA [0,1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 .
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12
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1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 1, 3, 3, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 1, 4, 6, 4, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 1, 5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0, 1, 6, 15, 20, 15, 6, 1, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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COMMENTS
| Triangle read by rows, Pascal's triangle (A007318) rows repeated .
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FORMULA
| T(n,k)=T(n-1,k)+((1+(-1)^n)/2)*T(n-1,k-1) .
G.f.: (1+x)/(1-(1+y)*x^2).
Sum_{k, 0<=k<=n} T(n,k)*x^k = A000012(n), A016116(n), A108411(n), A074872(n) for x = 0,1,2,4 respectively. - From DELEHAM Philippe, Nov 26 2011
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EXAMPLE
| Triangle begins :
1 ;
1, 0 ;
1, 1, 0 ;
1, 1, 0, 0 ;
1, 2, 1, 0, 0 ;
1, 2, 1, 0, 0, 0 ;
1, 3, 3, 1, 0, 0, 0 ;
1, 3, 3, 1, 0, 0, 0, 0 ;
1, 4, 6, 4, 1, 0, 0, 0, 0 ; ...
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CROSSREFS
| Cf. A007318, A064861, A152198(another version), A000931 (diagonal sums),A016116 (row sums)
Sequence in context: A035468 A051777 A107628 * A115296 A059048 A164116
Adjacent sequences: A152812 A152813 A152814 * A152816 A152817 A152818
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 13 2008
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EXTENSIONS
| Corrected example. Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 13 2008
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