A167230 - OEIS

%I #4 Aug 10 2015 00:29:38

%S 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,

%T 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,

%U 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

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

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

%e Triangle begins:

%e 1

%e 1 1

%e 1 0 1

%e 2 1 1 1

%e 1 0 0 0 1

%e 2 1 0 0 1 1

%e 2 0 1 0 1 0 1

%e 5 2 2 1 2 1 1 1

%e 1 0 0 0 0 0 0 0 1

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

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

%e 5 2 2 1 0 0 0 0 2 1 1 1

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

%e 5 2 0 0 2 1 0 0 2 1 0 0 1 1

%o (PARI) matexp(M) = sum(k=0,99,1./k!*M^k); matexps(M) = matexp(M)/exp(1);

%o matexpsb(M) = bestappr(matexps(M),9999);

%o P = matpascal(13); S = matrix(14,14, n,k, P[n,k]%p);

%o SS = matexpsb(S);

%o for(n=1,14,for(k=1,n,print1(SS[n,k]," "));print(""))

%Y Cf. A000110, A047999.

%K easy,nonn,tabl

%O 0,7

%A _Gerald McGarvey_, Oct 30 2009