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 A169689 (A169648(4n+4) - A147582(4n+5))/4. 4
 0, 1, 6, 4, 24, 4, 20, 12, 84, 4, 20, 12, 76, 12, 60, 36, 276, 4, 20, 12, 76, 12, 60, 36, 260, 12, 60, 36, 228, 36, 180, 108, 876, 4, 20, 12, 76, 12, 60, 36, 260, 12, 60, 36, 228, 36, 180, 108, 844, 12, 60, 36, 228, 36, 180, 108, 780, 36, 180, 108, 684, 108, 540, 324, 2724, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS A169648 and A147582 agree except at these terms. LINKS Table of n, a(n) for n=-1..64. David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.] N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS FORMULA a(-1)=0, a(0)=1, a(1)=6. For n >= 2, let n = 2^k+j with 0 <= j < 2^k, and write j+1 = 2^m*(2t+1). Then a(n) = 4*(3^(m+1)-2^(m+1))*3^wt(t), except if j=2^k-1 we must add 2^(k+1) to the result (here wt(t) = A000120(t)). Recurrence: a(-1)=0, a(0)=1, a(1)=6. For n>=2, write n = 2^k + j, with 0 <= j < 2^k. If j+1 is a power of 2, say j+1 = 2^r, set f=j+1 if r

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Last modified August 7 20:39 EDT 2024. Contains 375017 sequences. (Running on oeis4.)