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A081579
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Pascal-(1,4,1) array.
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8
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1, 1, 1, 1, 6, 1, 1, 11, 11, 1, 1, 16, 46, 16, 1, 1, 21, 106, 106, 21, 1, 1, 26, 191, 396, 191, 26, 1, 1, 31, 301, 1011, 1011, 301, 31, 1, 1, 36, 436, 2076, 3606, 2076, 436, 36, 1, 1, 41, 596, 3716, 9726, 9726, 3716, 596, 41, 1, 1, 46, 781, 6056, 21746, 33876, 21746, 6056
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| One of a family of Pascal-like arrays. A007318 is equivalent to the (1,0,1)-array. A008288 is equivalent to the (1,1,1)-array. Rows include A016861, A081587, A081588. Coefficients of the row polynomials in the Newton basis are given by A013612.
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REFERENCES
| Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
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FORMULA
| Square array T(n, k) defined by T(n, 0)=T(0, k)=1, T(n, k)=T(n, k-1)+4T(n-1, k-1)+T(n-1, k). Rows are the expansions of (1+4x)^k/(1-x)^(k+1).
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EXAMPLE
| Rows start
1 1 1 1 1 ...
1 6 11 16 21 ...
1 11 46 106 191 ...
1 16 106 396 1011 ...
1 21 191 1011 3606 ...
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CROSSREFS
| Cf. A081577, A081578, A081580.
Sequence in context: A046621 A046617 A131063 * A146772 A202868 A202877
Adjacent sequences: A081576 A081577 A081578 * A081580 A081581 A081582
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 23 2003
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