A167230 The matrix exponential of Sierpiński's triangle (A047999) scaled by exp(-1).

1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 1, 5, 2, 2, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 5, 2, 2, 1, 0, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 5, 2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 1, 1

Offset: 0

Author

Gerald McGarvey, Oct 30 2009

Keywords

• easy
• nonn
• tabl

Comments

Conjecture: All the nonzero entries in this triangle are Bell numbers (A000110).

Examples

			Triangle begins:
1
1 1
1 0 1
2 1 1 1
1 0 0 0 1
2 1 0 0 1 1
2 0 1 0 1 0 1
5 2 2 1 2 1 1 1
1 0 0 0 0 0 0 0 1
2 1 0 0 0 0 0 0 1 1
2 0 1 0 0 0 0 0 1 0 1
5 2 2 1 0 0 0 0 2 1 1 1
2 0 0 0 1 0 0 0 1 0 0 0 1
5 2 0 0 2 1 0 0 2 1 0 0 1 1
		

Crossrefs

Cf. A000110, A047999.

Programs

PARI

matexp(M) = sum(k=0,99,1./k!*M^k); matexps(M) = matexp(M)/exp(1);
matexpsb(M) = bestappr(matexps(M),9999);
P = matpascal(13); S = matrix(14,14, n,k, P[n,k]%p);
SS = matexpsb(S);
for(n=1,14,for(k=1,n,print1(SS[n,k]," "));print(""))