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A153342 Binomial transform of triangle A046854 (shifted). 3
1, 2, 0, 4, 1, 0, 8, 4, 1, 0, 16, 12, 5, 1, 0, 32, 32, 18, 6, 1, 0, 64, 80, 56, 25, 7, 1, 0, 128, 192, 160, 88, 33, 8, 1, 0, 256, 448, 432, 280, 129, 42, 9, 1, 0, 512, 1024, 1120, 832, 450, 180, 52, 10, 1, 0, 1024, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums = odd indexed Fibonacci numbers.

Mirror image of triangle in A121462 . [From Philippe Deléham, Dec 31 2008]

Triangle T(n,k), 0<=k<=n, read by rows given by [2,0,0,0,0,0,0,0,0,0,0,0,...] DELTA [0,1/2,1/2,0,0,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . [From Philippe Deléham, Jan 01 2009]

LINKS

Table of n, a(n) for n=0..65.

FORMULA

Triangle read by rows, A007318 * A046854 (shifted down 1 row, inserting a "1" at (0,0).

G.f.: (1-y*x)/(1-2*x-y*x+y*x^2) . - Philippe Deléham, Mar 27 2012

T(n,k) = 2*T(n-1,l) + T(n-1,k-1) - T(n-2,k-1), T(0,0) = 1, T(1,0) = 2, T(1,1) = 0 and T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 27 2012

EXAMPLE

First few rows of the triangle =

1;

2, 0;

4, 1, 0;

8, 4, 1, 0;

16, 12, 5, 1, 0;

32, 32, 18, 6, 1, 0;

64, 80, 56, 25, 7, 1, 0;

128, 192, 160, 88, 33, 8, 1, 0;

256, 448, 432, 280, 129, 42, 9, 1, 0;

512, 1024, 1120, 832, 450, 180, 52, 10, 1, 0;

...

CROSSREFS

Cf. A046854, A001519

Sequence in context: A291940 A153345 A140648 * A144258 A056859 A272098

Adjacent sequences:  A153339 A153340 A153341 * A153343 A153344 A153345

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Dec 24 2008

EXTENSIONS

Second term corrected by Philippe Deléham, Jan 01 2009

STATUS

approved

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Last modified December 13 17:30 EST 2017. Contains 295959 sequences.