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A355339 a(n) is the number of central even terms in the n-th row of triangle A355320; a(0) = 0.

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%I A355339 #10 Jun 29 2022 10:31:57
%S A355339 0,3,1,3,3,7,1,3,5,3,5,11,3,11,1,3,5,7,7,3,5,7,9,19,7,3,5,19,3,11,1,3,
%T A355339 5,7,9,11,13,11,7,3,5,7,9,11,13,15,17,35,15,11,7,3,5,7,9,35,7,3,5,19,
%U A355339 3,11,1,3,5,7,9,11,13,15,17,19,21,23,23,19,15
%N A355339 a(n) is the number of central even terms in the n-th row of triangle A355320; a(0) = 0.
%H A355339 Rémy Sigrist, <a href="/A355339/b355339.txt">Table of n, a(n) for n = 0..8192</a>
%F A355339 Conjecture: a(n) = 1 iff n > 0 and n belongs to A000918.
%e A355339 The first terms, alongside the corresponding rows of A355320, are:
%e A355339    n  a(n)  n-th row of A355320
%e A355339    -  ----  -------------------------------------------------------------
%e A355339    0     0                                1
%e A355339    1     3                          1 (0  0  0) 1
%e A355339    2     1                    1  0  0  1 (2) 1  0  0  1
%e A355339    3     3              1  0  0  2  3 (2  0  2) 3  2  0  0  1
%e A355339    4     3        1  0  0  3  4  3  1 (6  8  6) 1  3  4  3  0  0  1
%e A355339    5     7  1  0  0  4  5  4  3(12 16 12  6 12 16 12) 3  4  5  4  0  0  1
%o A355339 (PARI) { rr = 0; r = 1; for (n=0, 76, print1 (max(0, 2*valuation(r >> (2*n), 2)-1)", "); [rr, r] = [r, bitxor(bitxor(r, r<<4), bitxor(rr<<3, rr<<5))]) }
%Y A355339 Cf. A000918, A355320.
%K A355339 nonn
%O A355339 0,2
%A A355339 _Rémy Sigrist_, Jun 29 2022