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Search: id:A124182
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| 1, 0, 1, 0, 1, 2, 0, 0, 3, 4, 0, 0, 1, 8, 8, 0, 0, 0, 5, 20, 16, 0, 0, 0, 1, 18, 48, 32, 0, 0, 0, 0, 7, 56, 112, 64, 0, 0, 0, 0, 1, 32, 160, 256, 128, 0, 0, 0, 0, 0, 9, 120, 432, 576, 256, 0, 0, 0, 0, 0, 1, 50, 400, 1120, 1280, 512
(list; table; graph; listen)
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OFFSET
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0,6
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COMMENT
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Triangle T(n,k), 0<=k<=n, read by rows given by [0, 1, -1, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, 0, 0, 0, 0, 0, 0, 0,...] where DELTA is the operator defined in A084938 . Falling diagonal sums in A052980.
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FORMULA
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T(0,0)=T(1,1)=1, T(n,k)=0 if n<k or if k<0,T(n,k)=T(n-2,k-1)+2*T(n-1,k-1) . Sum_{k, 0<=k<=n}x^k*T(n,k)= (-1)^n*A090965(n), (-1)^n*A084120(n), (-1)^n*A006012(n), A033999(n), A000007(n), A001333(n), A084059(n) for x= -4, -3, -2, -1, 0, 1, 2 respectively . Sum_{k, 0<=k<=[n/2]} T(n-k,k)= Fibonacci(n-1)= A000045(n-1).
Sum_{k, 0<=k<=n}T(n,k)*x^(n-k)= A000012(n), A011782(n), A001333(n), A026150(n), A046717(n), A084057(n), A002533(n), A083098(n), A084058(n), A003665(n), A002535(n), A133294(n), A090042(n), A125816(n), A133343(n), A133345(n), A120612(n), A133356(n), A125818(n) for x= -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 respectively . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 26 2007
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 2;
0, 0, 3, 4;
0, 0, 1, 8, 8;
0, 0, 0, 5, 20, 16;
0, 0, 0, 1, 18, 48, 32;
0, 0, 0, 0, 7, 56, 112, 64;
0, 0, 0, 0, 1, 32, 160, 256, 128;
0, 0, 0, 0, 0, 9, 120, 432, 576, 256;
0, 0, 0, 0, 0, 1, 50, 400, 1120, 1280, 512;
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CROSSREFS
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Cf. A025192 (column sums).
Sequence in context: A053202 A050186 A074734 this_sequence A013585 A053653 A064146
Adjacent sequences: A124179 A124180 A124181 this_sequence A124183 A124184 A124185
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 05 2006
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