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Search: id:A121306
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| A121306 |
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Array read by antidiagonals: a(m,n) = a(m,n-1)+a(m-1,n) but with initialization values a(0,0)=0, a(m>=1,0)=1, a(0,1)=1, a(0,n>1)=0. |
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+0
4
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| 2, 2, 3, 2, 5, 4, 2, 7, 9, 5, 2, 9, 16, 14, 6, 2, 11, 25, 30, 20, 7, 2, 13, 36, 55, 50, 27, 8, 2, 15, 49, 91, 105, 77, 35, 9, 2, 17, 64, 140, 196, 182, 112, 44, 10, 19, 81, 204, 336, 378, 294, 156, 54, 100, 285, 540, 714, 672, 450, 210, 385, 825, 1254, 1386, 1122
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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For a(1,0)=1, a(m>1,0)=0 and a(0,n>=0)=0 one gets Pascal's triangle A007318.
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LINKS
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Thomas Wieder, Home Page.
Thomas Wieder, (Old) Home Page.
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FORMULA
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a(m,n) = a(m,n-1)+a(m-1,n), a(0,0)=0, a(m>=1,0)=1, a(0,1)=1, a(0,n>1)=0.
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EXAMPLE
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Array begins
2 2 2 2 2 2 2 2 2 ...
3 5 7 9 11 13 15 17 19 ...
4 9 16 25 36 49 64 81 100 ...
5 14 30 55 91 140 204 285 385 ...
6 20 50 105 196 336 540 825 1210 ...
7 27 77 182 378 714 1254 2079 3289 ...
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PROGRAM
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(Excel cell formula) =Z(-1)S+ZS(-1). The very first row (not included into the table) contains the initialization values: a(0, 1)=1, a(0, n>=2)=0. The very first column (not included into the table) contains the initialization values: a(m>=1, 0)=1. The value a(0, 0)=0 does not enter into the table.
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CROSSREFS
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The first nine rows are: A006527, A005408, A000290, A000330, A002415, A005585, A040977, A050486, A053347.
The initial columns are: A000027, A000096, A005581, A005582, A005583, A005584.
Cf. A119800, A007318, A006527, A005408, A000290, A000330, A002415, A005585, A040977, A050486, A053347, A000027, A000096, A005581, A005582, A005583, A005584.
Sequence in context: A111089 A051664 A029656 this_sequence A073311 A003974 A065769
Adjacent sequences: A121303 A121304 A121305 this_sequence A121307 A121308 A121309
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KEYWORD
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nonn,tabl
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AUTHOR
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Thomas Wieder (thomas.wieder(AT)t-online.de), Aug 04 2006, Aug 06 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2006
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