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 A071055 Number of 0's in n-th row of triangle in A071038. 1
 0, 0, 2, 0, 2, 2, 6, 0, 2, 2, 6, 2, 6, 6, 14, 0, 2, 2, 6, 2, 6, 6, 14, 2, 6, 6, 14, 6, 14, 14, 30, 0, 2, 2, 6, 2, 6, 6, 14, 2, 6, 6, 14, 6, 14, 14, 30, 2, 6, 6, 14, 6, 14, 14, 30, 6, 14, 14, 30, 14, 30, 30, 62, 0, 2, 2, 6, 2, 6, 6, 14, 2, 6, 6, 14, 6, 14, 14, 30, 2, 6, 6, 14, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is also the number of pairs of consecutive entries in the n-th row of Pascal's triangle with opposite parity. All terms appear to be of the form 2^k - 2 (checked for n <= 10000). - Michael De Vlieger, Mar 02 2015 This appears to be equal to the number of previous values k, from 1..n-1, such that k AND n = k, where 'AND' is binary AND, and where the sequence starts at 1. For example, 1 AND 2 = 0, so a(2) = 0, while 1 AND 3 = 1 and 2 AND 3 = 2, so a(3) = 2. It follows from this that if n = 2^m - 1 then a(n) = n - 1 = 2^m - 2, giving the right border values noted below. - Scott R. Shannon, Apr 19 2023 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 0..10000 Eric Weisstein's World of Mathematics, Rule 182 Index entries for sequences related to cellular automata FORMULA a(n)=b(n+1), with b(0)=0, b(2n)=b(n), b(2n+1)=2b(n)+2-2[n==0] (conjectured). - Ralf Stephan, Mar 05 2004 a(n) = pext(n, n + 1) (conjectured) where pext is the "parallel bits extract" instruction of the x86 CPU; pext(x, mask) extracts bits from x at the bit locations specified by mask to contiguous low bits. - Falk Hüffner, Jul 26 2019 EXAMPLE From Omar E. Pol, Mar 02 2015: (Start) Also, written as an irregular triangle in which the row lengths are the powers of 2, the sequence begins: 0; 0,2; 0,2,2,6; 0,2,2,6,2,6,6,14; 0,2,2,6,2,6,6,14,2,6,6,14,6,14,14,30; 0,2,2,6,2,6,6,14,2,6,6,14,6,14,14,30,2,6,6,14,6,14,14,30,6,14,14,30,14,30,30,62; ... It appears that the right border gives the nonnegative terms of A000918. It appears that the row sums give A056182. (End) MATHEMATICA Count[#, n_ /; n == 0] & /@ Flatten[CellularAutomaton[182, {{1}, 0}, {{#}}] & /@ Range[0, 100], 1] (* Michael De Vlieger, Mar 02 2015 *) PROG (PARI) A011371(n)=my(s); while(n>>=1, s+=n); s a(n)=my(t=A011371(n)); sum(k=1, n, (A011371(k)+A011371(n-k)==t)!=(A011371(k-1)+A011371(n-k+1)==t)) \\ Charles R Greathouse IV, Mar 02 2015 CROSSREFS Cf. A071042. Sequence in context: A301823 A301999 A171936 * A183034 A354101 A078052 Adjacent sequences: A071052 A071053 A071054 * A071056 A071057 A071058 KEYWORD nonn AUTHOR Hans Havermann, May 26 2002 STATUS approved

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Last modified December 6 08:34 EST 2023. Contains 367600 sequences. (Running on oeis4.)