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A038763 Triangular matrix arising in enumeration of catafusenes, read by rows. 8
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; text; internal format)
OFFSET

0,5

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. - Philippe Deléham, Aug 10 2005

Mirror image of A136158. - Philippe Deléham, 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, Jul 19 2008

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. - Clark Kimberling, Aug 04 2011

REFERENCES

S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.

LINKS

Table of n, a(n) for n=0..56.

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 Deléham, Sep 22 2006

T(n,k) = A136158(n,n-k). - Philippe Deléham, Dec 17 2007

G.f.: (-1+2*x*y)/(-1+3*x*y+x). - R. J. Mathar, Aug 11 2015

EXAMPLE

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,

CROSSREFS

Cf. A024462.

Sequence in context: A127673 A016698 A200115 * A200384 A128007 A098458

Adjacent sequences:  A038760 A038761 A038762 * A038764 A038765 A038766

KEYWORD

tabl,nonn,easy

AUTHOR

N. J. A. Sloane, May 03 2000

STATUS

approved

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Last modified February 22 06:22 EST 2019. Contains 320389 sequences. (Running on oeis4.)