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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,14

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..136.

FORMULA

T(n,k) = A008302(k-2,n-k), n>=k>1. - R. J. Mathar, Dec 15 2010

EXAMPLE

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

MATHEMATICA

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 *)

PROG

(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))

CROSSREFS

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

Sequence in context: A116402 A093323 A106278 * A227819 A064287 A196389

Adjacent sequences:  A177514 A177515 A177516 * A177518 A177519 A177520

KEYWORD

nonn,tabl

AUTHOR

Mats Granvik, Roger L. Bagula, Dec 11 2010

STATUS

approved

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Last modified November 20 04:05 EST 2017. Contains 294959 sequences.