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A167230 The matrix exponential of Sierpiński's triangle (A047999) scaled by exp(-1). 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A309144 A085425 A244250 * A093658 A096493 A269242

Adjacent sequences:  A167227 A167228 A167229 * A167231 A167232 A167233

KEYWORD

easy,nonn,tabl

AUTHOR

Gerald McGarvey, Oct 30 2009

STATUS

approved

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Last modified January 22 07:31 EST 2022. Contains 350481 sequences. (Running on oeis4.)