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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 #10 Jun 29 2022 10:31:57

%S 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 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 3,11,1,3,5,7,9,11,13,15,17,19,21,23,23,19,15

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

%H Rémy Sigrist, <a href="/A355339/b355339.txt">Table of n, a(n) for n = 0..8192</a>

%F Conjecture: a(n) = 1 iff n > 0 and n belongs to A000918.

%e The first terms, alongside the corresponding rows of A355320, are:

%e n a(n) n-th row of A355320

%e - ---- -------------------------------------------------------------

%e 0 0 1

%e 1 3 1 (0 0 0) 1

%e 2 1 1 0 0 1 (2) 1 0 0 1

%e 3 3 1 0 0 2 3 (2 0 2) 3 2 0 0 1

%e 4 3 1 0 0 3 4 3 1 (6 8 6) 1 3 4 3 0 0 1

%e 5 7 1 0 0 4 5 4 3(12 16 12 6 12 16 12) 3 4 5 4 0 0 1

%o (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 Cf. A000918, A355320.

%K nonn

%O 0,2

%A _Rémy Sigrist_, Jun 29 2022