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A125105
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Triangular array with the first half of the odd-indexed rows of A048004.
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2
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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; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| A000079 counts compositions admitting a variety of triangular views; for example A048004 and A105147. The sub-table formed from the odd rows of A048004 have row sum 1,8,44,208,912,... Because only the first half of rows of A048004 is transferred to this triangle here, there is a difference between row sums of A048004 and row sums here, A045623(n-1).
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FORMULA
| T(n,k) = A048004(2*n-1,k), 0<=k<n. - R. J. Mathar, Nov 23 2007
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EXAMPLE
| The odd indexed rows of triangle A048004 begin
1 1
1 4 2 1
1 12 11 5 2 1
etc.
so the triangle here begins
1
1 4
1 12 11
etc.
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MAPLE
| A048004 := proc(n, k) option remember ; if k < 0 or k > n then 0; elif k = 0 or k = n then 1; else 2*procname(n-1, k)+procname(n-1, k-1)-2*procname(n-2, k-1)+procname(n-k-1, k-1)-procname(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, Nov 23 2007
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CROSSREFS
| Cf. A008464 (row sums), A008464, A045623, A048004, A105147, A125104.
Sequence in context: A130322 A106194 A051290 * A144878 A049424 A157394
Adjacent sequences: A125102 A125103 A125104 * A125106 A125107 A125108
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Dec 07 2006
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 23 2007
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