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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 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.)