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A156348
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Triangle T(n,k) read by rows. Column of Pascal's triangle interleaved with k-1 zeros.
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10
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1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 0, 0, 1, 1, 3, 3, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 4, 0, 4, 0, 0, 0, 1, 1, 0, 6, 0, 0, 0, 0, 0, 1, 1, 5, 0, 0, 5, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 6, 10, 10, 0, 6, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 7, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,8
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COMMENTS
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The rows of the Pascal triangle are here found as square root parabolas like in the plots at www.divisorplot.com. Central binomial coefficients are found at the square root boundary.
A156348 * A000010 = A156834: (1, 2, 3, 5, 5, 12, 7, 17, 19, 30, 11,...). [From Gary W. Adamson, Feb 16 2009]
Row sums give A157019.
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REFERENCES
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el Houcein el Abdalaoui, Mohamed Dahmoune and Djelloul Ziadi, On the transition reduction problem for finite automata, arXiv preprint arXiv:1301.3751, 2013. - From N. J. A. Sloane, Feb 12 2013
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LINKS
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Table of n, a(n) for n=1..104.
Jeff Ventrella, Divisor Plot
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EXAMPLE
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Table begins:
1
1..1
1..0..1
1..2..0..1
1..0..0..0..1
1..3..3..0..0..1
1..0..0..0..0..0..1
1..4..0..4..0..0..0..1
1..0..6..0..0..0..0..0..1
1..5..0..0..5..0..0..0..0..1
1..0..0..0..0..0..0..0..0..0..1
1..6..10.10.0..6..0..0..0..0..0..1
1..0..0..0..0..0..0..0..0..0..0..0..1
1..7..0..0..0..0..7..0..0..0..0..0..0..1
1..0..15.0..15.0..0..0..0..0..0..0..0..0..1
1..8..0..20.0..0..0..8..0..0..0..0..0..0..0..1
1..0..0..0..0..0..0..0..0..0..0..0..0..0..0..0..1
1..9..21.0..0..21.0..0..9..0..0..0..0..0..0..0..0..1
1..0..0..0..0..0..0..0..0..0..0..0..0..0..0..0..0..0..1
1..10.0..35.35.0..0..0..0..10..0..0..0..0..0..0..0..0..0..1
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MAPLE
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A156348 := proc(n, k)
if k < 1 or k > n then
return 0 ;
elif n mod k = 0 then
binomial(n/k-2+k, k-1) ;
else
0 ;
end if;
end proc: # R. J. Mathar, Mar 03 2013
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CROSSREFS
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Cf. A007318, A051731.
Cf. A156834 [From Gary W. Adamson, Feb 16 2009]
Sequence in context: A216282 A147861 A167271 * A101614 A051659 A085861
Adjacent sequences: A156345 A156346 A156347 * A156349 A156350 A156351
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Mats Granvik, Feb 08 2009
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STATUS
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approved
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