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Search: id:A062111
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| A062111 |
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Upper-right triangle resulting from binomial transform calculation for nonnegative integers. |
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+0
9
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| 0, 1, 1, 4, 3, 2, 12, 8, 5, 3, 32, 20, 12, 7, 4, 80, 48, 28, 16, 9, 5, 192, 112, 64, 36, 20, 11, 6, 448, 256, 144, 80, 44, 24, 13, 7, 1024, 576, 320, 176, 96, 52, 28, 15, 8, 2304, 1280, 704, 384, 208, 112, 60, 32, 17, 9, 5120, 2816, 1536, 832, 448, 240, 128, 68, 36, 19, 10
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Comment from Philippe DELEMAM, Apr 15 2007 (Start)
This triangle can be found in the Laisant reference in the following form:
...............................5...11
..........................4...9...20
.....................3...7..16...36
................2...5..12..28.....
...........1...3...8..20..48.....
......0...1...4..12..32..80...... (End)
Triangle A152920 reversed . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 21 2009]
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REFERENCES
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C.-A. Laisant, Sur les tableaux de sommes - Nouvelles applications, Compt. Rendus de l'Association Francaise pour l'Avancement des Sciences, Aout. 04, 1893, p. 212.
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LINKS
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F. Ellermann, Illustration of binomial transforms
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FORMULA
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a(n, n)=n; a(n, k)=a(n, k-1)+a(n+1, k) if k>n. a(n, k)=(k+n)*2^(k-n-1) if k >= n.
T(2n,n)= 3*n*2^(n-1) = 3*A001787(n) . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 21 2009]
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EXAMPLE
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Rows start (0,1,4,12,32,...), (1,3,8,20,...), (2,5,12,...), (3,7,...), etc.
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CROSSREFS
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Rows include (essentially) A001787, A001792, A045623, A045891, A034007. Diagonals include (essentially) A001477, A005408, A008586, A017113, A017113, A008598. Column sums are A058877.
Cf. A111297, A159694, A159695, A159696, A159697 [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 21 2009]
Sequence in context: A105109 A065367 A033882 this_sequence A033881 A099406 A061312
Adjacent sequences: A062108 A062109 A062110 this_sequence A062112 A062113 A062114
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), May 30 2001
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