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Search: id:A125105
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| 1, 1, 4, 1, 12, 11, 1, 33, 47, 27, 1, 88, 185, 127, 63, 1, 232, 694, 563, 303, 143, 1, 609, 2526, 2400, 1394, 687, 319, 1, 1596, 9012, 9960, 6215, 3186, 1519, 703, 1, 4180, 31709, 40534, 27095, 14401, 7026, 3311, 1535, 1, 10945, 110469, 162538, 116143
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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A000079 counts compositions admitting a variety of triagular views; for example A048004 and A105147. The sub-table formed from the odd rows of A048004 have row sum 1,8,44,208,912,... and the remaining locations repeat sequence A045623.
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FORMULA
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T(n,k) = A048004(2*n-1,k), 0<=k<n. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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EXAMPLE
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The even rows of Table A048004 begin
1 1
1 4 2 1
1 12 11 5 2 1
etc.
so A125105 begins
1
1 4
1 12 11
etc.
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MAPLE
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A048004 := proc(n, k) option remember ; if k < 0 or k > n then 0; elif k = 0 or k = n then 1; else 2*A048004(n-1, k)+A048004(n-1, k-1)-2*A048004(n-2, k-1)+A048004(n-k-1, k-1)-A048004(n-k-2, k) ; fi ; end: A125105 := proc(n, k) A048004(2*n-1, k) ; end: for n from 1 to 13 do for k from 0 to n-1 do printf("%d ", A125105(n, k)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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CROSSREFS
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Cf. A000079 A008464 A045623 A048004 A105147 A125104.
Sequence in context: A130322 A106194 A051290 this_sequence A144878 A049424 A157394
Adjacent sequences: A125102 A125103 A125104 this_sequence A125106 A125107 A125108
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KEYWORD
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easy,nonn,tabl,uned
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Dec 07 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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