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A038763
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Triangular matrix arising in enumeration of catafusenes, read by rows.
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9
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1, 1, 1, 1, 4, 3, 1, 7, 15, 9, 1, 10, 36, 54, 27, 1, 13, 66, 162, 189, 81, 1, 16, 105, 360, 675, 648, 243, 1, 19, 153, 675, 1755, 2673, 2187, 729, 1, 22, 210, 1134, 3780, 7938, 10206, 7290, 2187, 1, 25, 276, 1764, 7182, 19278, 34020, 37908, 24057, 6561, 1, 28
(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, given by [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938 . - DELEHAM Philippe (kolotoko(aT)lagoon.nc), Aug 10 2005
Mirror image of A136158 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 17 2007
Triangle read by rows, n-th row = X^(n-1) * [1, 1, 0, 0, 0,...] where X = an infinite bidiagonal matrix with (1,1,1,...) in the main diagonal and (3,3,3,..) in the subdiagonal; given row 0 = 1. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008
A038763=fusion of polynomial sequences P and Q given by p(n,x)=(x+2)^n and q(n,x)=(2x+1)^n; see A193722 for the definition of fusion of two sequences of polynomials or triangular arrays. [From Clark Kimberling, Aug 4 2011]
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REFERENCES
| S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.
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FORMULA
| a(n, 0)=1; a(1, 1)=1; a(n, k)=0 for k>n; a(n, k)=a(n-1, k-1)*3+a(n-1, k) for n >= 2.
Sum_[k, 0<=k<=n} T(n,k)= A081294(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 22 2006
T(n,k)=A136158(n,n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 17 2007
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EXAMPLE
| 1; 1,1; 1,4,3; 1,7,15,9; ...
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CROSSREFS
| Cf. A024462.
Sequence in context: A127673 A016698 A200115 * A200384 A128007 A098458
Adjacent sequences: A038760 A038761 A038762 * A038764 A038765 A038766
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KEYWORD
| tabl,nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 03 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000
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