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

0,7

Comments

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

Links

Table of n, a(n) for n=0..104.

Example

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

Prog

(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(""))

Crossrefs

Cf. A000110, A047999.

Sequence in context: A085425 A355685 A244250 * A093658 A096493 A269242

Adjacent sequences: A167227 A167228 A167229 * A167231 A167232 A167233

Keyword

easy,nonn,tabl

Author

Gerald McGarvey, Oct 30 2009

Status

approved