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A177517 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. 6

%I

%S 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,

%T 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,

%U 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

%N 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.

%C A008302 is the main entry for this triangle.

%C Essentially A060701 which is equal to this table beginning from the second column.

%C The recurrence formula is similar to the recurrence for A177978.

%H Alois P. Heinz, <a href="/A177517/b177517.txt">Table of n, a(n) for n = 1..20301</a>

%F T(n,k) = A008302(k-2,n-k), n>=k>1. - _R. J. Mathar_, Dec 15 2010

%e 1,

%e 0,1,

%e 0,0,1,

%e 0,0,1,1,

%e 0,0,0,2,1,

%e 0,0,0,2,3,1,

%e 0,0,0,1,5,4,1,

%e 0,0,0,0,6,9,5,1,

%e 0,0,0,0,5,15,14,6,1,

%e 0,0,0,0,3,20,29,20,7,1,

%e 0,0,0,0,1,22,49,49,27,8,1

%t 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 *)

%o (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))

%o (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))

%Y Cf. A008302, A060701, A177978, A175105. Column sums are A000142. Row sums are A008930.

%K nonn,tabl

%O 1,14

%A _Mats Granvik_, _Roger L. Bagula_, Dec 11 2010

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Last modified August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)