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Search: id:A061290
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| A061290 |
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Square array read by antidiagonals of T(n,k)=T(n-1,k)+T(n-1,[k/2]) with T(0,0)=1. |
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+0
2
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| 1, 0, 2, 0, 1, 4, 0, 0, 3, 8, 0, 0, 1, 7, 16, 0, 0, 1, 4, 15, 32, 0, 0, 0, 4, 11, 31, 64, 0, 0, 0, 1, 11, 26, 63, 128, 0, 0, 0, 1, 5, 26, 57, 127, 256, 0, 0, 0, 1, 5, 16, 57, 120, 255, 512, 0, 0, 0, 1, 5, 16, 42, 120, 247, 511, 1024, 0, 0, 0, 0, 5, 16, 42, 99, 247, 502, 1023, 2048, 0, 0
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Row sum is 3^n.
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FORMULA
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T(n, k) =C(n, 0)+C(n, 1)+...+C(n, n-ceiling[log2(k+1)]) =2^n-C(n, 0)-C(n, 1)-...-C(n, floor[log2(k)]) =A008949(n, n-A029837(k+1)) =A000079(n)-A008949(n, A000523(k)).
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EXAMPLE
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T(9,3)=T(8,3)+T(8,[3/2])=T(8,3)+T(8,1)=247+255=502. Rows start (1,0,0,0,0,...), (2,1,0,0,0,...), (4,3,1,1,0,...), (8,7,4,4,1,...), etc.
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CROSSREFS
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Row sums are A000244. Columns are A000079, A000225, A000295 twice, A002662 four times, A002663 eight times, A002664 sixteen times, A035038 thirty two times etc.
Sequence in context: A062104 A018843 A072737 this_sequence A099096 A099089 A121298
Adjacent sequences: A061287 A061288 A061289 this_sequence A061291 A061292 A061293
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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 22 2001
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