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A124788
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Triangle read by rows: expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2).
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5
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1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 0, 0, 0, 0, 3, 3, 1, 0, 0, 0, 0, 0, 0, 1, 3, 4, 1, 0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 6, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 10, 10, 6
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,20
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COMMENTS
| Row sums give A000931(n+5). Diagonal sums are A124789.
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FORMULA
| Number triangle T(n,k)=C(floor(k/2),n-k)
Column k has g.f. x^k*(1+x)^floor(k/2) - Paul Barry (pbarry(AT)wit.ie), Feb 01 2007
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EXAMPLE
| Triangle begins
1,
0, 1,
0, 0, 1,
0, 0, 1, 1,
0, 0, 0, 1, 1,
0, 0, 0, 0, 2, 1,
0, 0, 0, 0, 1, 2, 1,
0, 0, 0, 0, 0, 1, 3, 1,
0, 0, 0, 0, 0, 0, 3, 3, 1,
0, 0, 0, 0, 0, 0, 1, 3, 4, 1,
0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 1
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MAPLE
| A124788 := proc(n, k) binomial(floor(k/2), n-k) ; end: for n from 0 to 20 do for k from 0 to n do printf("%d, ", A124788(n, k)) ; od ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 10 2007
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CROSSREFS
| Cf. A124745.
Sequence in context: A072612 A116378 A124744 * A017857 A127842 A127512
Adjacent sequences: A124785 A124786 A124787 * A124789 A124790 A124791
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Nov 07 2006
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 10 2007
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