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Search: id:A133367
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| A133367 |
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Triangle T(n,k) read by rows given by [2,1,2,1,2,1,2,1,2,1,2,1,...] DELTA [1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . |
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1
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| 1, 2, 1, 6, 5, 1, 22, 23, 8, 1, 90, 107, 49, 11, 1, 394, 509, 276, 84, 14, 1, 1806, 2473, 1505, 556, 128, 17, 1, 8558, 12235, 8100, 3429, 974, 181, 20, 1, 41586, 61463, 43393, 20355, 6713, 1557, 243, 23, 1
(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 begins : 1 ; 2, 1 6, 5, 1 ; 22, 23, 8, 1 ; 90, 107, 49, 11, 1 ; 394, 509, 276, 84, 14, 1 ; 1806, 2473, 1505, 556, 128, 17, 1 ; 8558, 12235, 8100, 3429, 974, 181, 20, 1 ; 41586, 61463, 43393, 20355, 6713, 1557, 243, 23, 1 ; ...
Contribution from Paul Barry (pbarry(AT)wit.ie), Apr 28 2009: (Start)
Riordan array ((1-x-sqrt(1-6x+x^2))/(2x), (1-3x-sqrt(1-6x+x^2))/(4x)).
Inverse of Riordan array (1/(1+2x),x/(1+3x+2x^2)) (a signed version of A124237). (End)
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FORMULA
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T(0,0)=1 ; T(n,k)=0 if k<0 or if k>n ; T(n,0) = 2*T(n-1,0)+2*T(n-1,1) ; T(n,k) = T(n-1,k-1)+3*T(n-1,k)+2*T(n-1,k+1) for k>=1 .
G.f.: 1/(1-xy-2x-x^2(2+y)/(1-3x-2x^2/(1-3x-2x^2/(1-3x-2x^2/(1- ... (continued fraction) [From Paul Barry (pbarry(AT)wit.ie), Apr 28 2009]
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EXAMPLE
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Contribution from Paul Barry (pbarry(AT)wit.ie), Apr 28 2009: (Start)
Triangle begins
1,
2, 1,
6, 5, 1,
22, 23, 8, 1,
90, 107, 49, 11, 1,
394, 509, 276, 84, 14, 1,
1806, 2473, 1505, 556, 128, 17, 1
Production matrix begins
2, 1,
2, 3, 1,
0, 2, 3, 1,
0, 0, 2, 3, 1,
0, 0, 0, 2, 3, 1,
0, 0, 0, 0, 2, 3, 1,
0, 0, 0, 0, 0, 2, 3, 1; (End)
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CROSSREFS
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Cf.: A006318, A000012, A016789.
Sequence in context: A159965 A116395 A159924 this_sequence A121576 A121575 A049444
Adjacent sequences: A133364 A133365 A133366 this_sequence A133368 A133369 A133370
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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), Oct 27 2007
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