A155102 Triangle T(n,k) read by rows. If n=k then T(n,k)=1, elseif n=2*k then T(n,k)=-(k+1), else T(n,k)=0.

1, -2, 1, 0, 0, 1, 0, -3, 0, 1, 0, 0, 0, 0, 1, 0, 0, -4, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -6, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -7, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0

Offset

1,2

Comments

Matrix inverse of this triangle is A155103.

Links

Table of n, a(n) for n=1..102.

Example

Table begins:
1,
-2,1,
0,0,1,
0,-3,0,1,
0,0,0,0,1,
0,0,-4,0,0,1,
0,0,0,0,0,0,1,
0,0,0,-5,0,0,0,1,

Mathematica

t[n_, k_] := Which[n == k, 1, n == 2k, -k - 1, True, 0]; Flatten[ Table[t[n, k], {n, 1, 14}, {k, 1, n}]] (* Jean-François Alcover, Jul 19 2012 *)

Prog

(PARI) T(n, k)=if(n==k, 1, if(n==2*k, -(k+1))); for(n=1, 20, for(k=1, n, print1(T(n, k), ", ")); print())
(Excel) =if(row()=column(); 1; if(and(row()>=column()*2; row()<=column()*2); -1; 0))*(row()-column()+1)

Crossrefs

Cf. A155103.

Sequence in context: A056560 A345415 A096608 * A237621 A214625 A363339

Adjacent sequences: A155099 A155100 A155101 * A155103 A155104 A155105

Keyword

sign,tabl

Author

Mats Granvik, Jan 20 2009

Extensions

Definition clarified by Mats Granvik, Dec 05 2010

Status

approved