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A177517
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Triangle T(n,k) read by rows defined by recurrence T(n,1)=A000007(n-1) and T(n,k) = sum_{i=1..k-1} T(n-i,k-1) if k>1.
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6
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1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 3, 1, 0, 0, 0, 1, 5, 4, 1, 0, 0, 0, 0, 6, 9, 5, 1, 0, 0, 0, 0, 5, 15, 14, 6, 1, 0, 0, 0, 0, 3, 20, 29, 20, 7, 1, 0, 0, 0, 0, 1, 22, 49, 49, 27, 8, 1, 0, 0, 0, 0, 0, 20, 71, 98, 76, 35, 9, 1, 0, 0, 0, 0, 0, 15, 90, 169, 174, 111, 44, 10, 1, 0, 0, 0, 0, 0, 9, 101, 259, 343, 285, 155, 54, 11, 1, 0, 0, 0, 0, 0, 4, 101, 359, 602, 628, 440, 209, 65, 12, 1, 0, 0, 0, 0, 0, 1, 90, 455, 961, 1230, 1068, 649, 274, 77, 13, 1
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OFFSET
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1,14
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COMMENTS
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A008302 is the main entry for this triangle.
Essentially A060701 which is equal to this table beginning from the second column.
The recurrence formula is similar to the recurrence for A177978.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..20301
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FORMULA
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T(n,k) = A008302(k-2,n-k), n>=k>1. - R. J. Mathar, Dec 15 2010
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EXAMPLE
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1,
0,1,
0,0,1,
0,0,1,1,
0,0,0,2,1,
0,0,0,2,3,1,
0,0,0,1,5,4,1,
0,0,0,0,6,9,5,1,
0,0,0,0,5,15,14,6,1,
0,0,0,0,3,20,29,20,7,1,
0,0,0,0,1,22,49,49,27,8,1
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MATHEMATICA
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Clear[t]; t[1, 1] = 1; t[n_, 1] = 0; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}], 0]; Flatten[Table[t[n, k], {n, 12}, {k, n}]] (* Robert G. Wilson v, Jun 24 2011 *) (* Added the necessary If condition, Mats Granvik, Jan 23 2012 *)
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PROG
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(Excel cell formula, American) =if(column()=1, if(row()=1, 1, 0), if(row()>=column(), sum(indirect(address(row()-column()+1, column()-1, 4)&":"&address(row()-column()+column()-1, column()-1, 4), 4)), 0))
(Excel cell formula, European) =if(column()=1; if(row()=1; 1; 0); if(row()>=column(); sum(indirect(address(row()-column()+1; column()-1; 4)&":"&address(row()-column()+column()-1; column()-1; 4); 4)); 0))
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CROSSREFS
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Cf. A008302, A060701, A177978, A175105. Column sums are A000142. Row sums are A008930.
Sequence in context: A093323 A106278 A339829 * A227819 A064287 A196389
Adjacent sequences: A177514 A177515 A177516 * A177518 A177519 A177520
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KEYWORD
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nonn,tabl
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AUTHOR
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Mats Granvik, Roger L. Bagula, Dec 11 2010
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STATUS
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approved
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