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Search: id:A126791
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| 1, 4, 1, 17, 7, 1, 75, 39, 10, 1, 339, 202, 70, 13, 1, 1558, 1015, 425, 110, 16, 1, 7247, 5028, 2400, 771, 159, 19, 1, 34016, 24731, 12999, 4872, 1267, 217, 22, 1, 160795, 121208, 68600, 28882, 8890, 1940, 284, 25, 1, 764388, 593019, 354890, 164136
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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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)=4*T(n-1,0)+T(n-1,1), T(n,k)=T(n-1,k-1)+3*T(n-1,k)+T(n-1,k+1) for k>=1.
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
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Sum{k, k>=0}T(m,k)*T(n,k)=T(m+n,0)=A026378(m+n+1) . Sum{k, 0<=k<=n}T(n,k)=5^n=A000351(n).
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EXAMPLE
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Triangle begins:
1;
4, 1;
17, 7, 1;
75, 39, 10, 1;
339, 202, 70, 13, 1;
1558, 1015, 425, 110, 16, 1;
7247, 5028, 2400, 771, 159, 19, 1;
34016, 24731, 12999, 4872, 1267, 217, 22, 1;...
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CROSSREFS
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Sequence in context: A111661 A072651 A093035 this_sequence A052179 A126331 A013631
Adjacent sequences: A126788 A126789 A126790 this_sequence A126792 A126793 A126794
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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), Mar 14 2007
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