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Search: id:A082233
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| A082233 |
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In the following square array numbers are entered like this a(1,1),a(1,2),a(2,1),a(3,1),a(2,2),a(1,3),a(1,4),a(2,3),a(3,2),a(4,1),a(5,1),a(4,2),... such that every entry is the arithmetic mean of the two diametrically opposite neighbors ( wherever a pair exists). 1 2 3 4 5 6 7... 3 4 5 6 7 8 9... 5 6 7 8 9 10 11... 7 8 9 10 11 12 13... 9 10 11 12 13 14 15... ... Sequence contains the numbers as they are entered. |
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+0
2
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| 1, 2, 3, 5, 4, 3, 4, 5, 6, 7, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 13, 12, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 13, 14, 15
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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1. The n-th row contains natural numbers starting from 2n+1. 2. The 2n-th column contains natural numbers beginning with 2n. 3. The (2n-1)-th column contains odd number beginning with 2n-1. 4. The n-th antidigonal sum is given by pentagonal number A000326(n+1). 5. The main diagonal is given by A016777.
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EXAMPLE
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In the following square array numbers are entered like this a(1,1),a(1,2),a(2,1),a(3,1),a(2,2),a(1,3),a(1,4),a(2,3),a(3,2),a(4,1),a(5,1),a(4,2),...
such that every entry is the arithmetic mean of the two diametrically opposite neighbors ( wherever a pair exists).
1 2 3 4 5 6 7...
3 4 5 6 7 8 9...
5 6 7 8 9 10 11...
7 8 9 10 11 12 13...
9 10 11 12 13 14 15...
...
Sequence contains the numbers as they are entered.
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CROSSREFS
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Cf. A000326, A016777, A082234.
Adjacent sequences: A082230 A082231 A082232 this_sequence A082234 A082235 A082236
Sequence in context: A021981 A068508 A137403 this_sequence A058981 A117339 A096016
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KEYWORD
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easy,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 10 2003
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