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A126093
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Inverse binomial matrix applied to A110877.
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28
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1, 0, 1, 1, 2, 1, 2, 6, 4, 1, 6, 18, 15, 6, 1, 18, 57, 54, 28, 8, 1, 57, 186, 193, 118, 45, 10, 1, 186, 622, 690, 474, 218, 66, 12, 1, 622, 2120, 2476, 1856, 976, 362, 91, 14, 1, 2120, 7338, 8928, 7164, 4170, 1791, 558, 120, 16, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Triangle T(n,k), 0<=k<=n, read by rows defined by : T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,0)=T(n-1,1), T(n,k)=T(n-1,k-1)+2*T(n-1,k)+T(n-1,k+1) for k>=1.
Diagonal sums are A065601 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 05 2007
This triangle belongs to the family of triangles defined by: T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,0)=x*T(n-1,0)+T(n-1,1), T(n,k)=T(n-1,k-1)+y*T(n-1,k)+T(n-1,k+1) for k>=1 . Other triangles arise by choosing different values for (x,y): (0,0) -> A053121; (0,1) -> A089942; (0,2) -> A126093; (0,3) -> A126970; (1,0)-> A061554; (1,1) -> A064189; (1,2) -> A039599; (1,3) -> A110877; ((1,4) -> A124576; (2,0) -> A126075; (2,1) -> A038622; (2,2) -> A039598; (2,3) -> A124733; (2,4) -> A124575; (3,0) -> A126953; (3,1) -> A126954; (3,2) -> A111418; (3,3) -> A091965; (3,4) -> A124574; (4,3) -> A126791; (4,4) -> A052179; (4,5) -> A126331; (5,5) -> A125906 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 25 2007
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FORMULA
| Sum_{k, 0<=k<=n}T(m,k)*T(n,k)=T(m+n,0)=A000957(m+n+1).
Sum[k, 0<=k<=n-1}A126093(n,k)=A026641(n), for n>=1 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 05 2007
Sum_{k, 0<=k<=n}T(n,k)*(3k+1)=4^n . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 22 2007
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EXAMPLE
| Triangle begins:
1;
0, 1;
1, 2, 1;
2, 6, 4, 1;
6, 18, 15, 6, 1;
18, 57, 54, 28, 8, 1;
57, 186, 193, 118, 45, 10, 1;
186, 622, 690, 474, 218, 66, 12, 1;
622, 2120, 2476, 1856, 976, 362, 91, 14, 1;
2120, 7338, 8928, 7164, 4170, 1791, 558, 120, 16, 1;
Production matrix begins
0, 1
1, 2, 1
0, 1, 2, 1
0, 0, 1, 2, 1
0, 0, 0, 1, 2,1
0, 0, 0, 0, 1, 2, 1
0, 0, 0, 0, 0, 1, 2, 1
0, 0, 0, 0, 0, 0, 1, 2, 1
0, 0, 0, 0, 0, 0, 0, 1, 2, 1
- From DELEHAM Philippe, Nov 07 2011
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CROSSREFS
| Sequence in context: A099206 A121341 A174959 * A065279 A151962 A072137
Adjacent sequences: A126090 A126091 A126092 * A126094 A126095 A126096
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 03 2007
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