A268292 a(n) is the total number of isolated 1's at the boundary between n-th and (n-1)-th iterations in the pattern of A267489.

0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 7, 9, 11, 14, 18, 22, 26, 30, 34, 39, 45, 51, 57, 63, 69, 76, 84, 92, 100, 108, 116, 125, 135, 145, 155, 165, 175, 186, 198, 210, 222, 234, 246, 259, 273, 287, 301, 315, 329, 344, 360, 376, 392, 408, 424, 441

Offset

0,9

Comments

Refer to pattern of A267489, The total number of isolated 1's is a(n) and A112421 when consider at the boundary between n-th and (n-1)-th iterations and at the boundary in the same iterations concatenate on horizontal respectively. See illustrations in the links.

Empirically, a(n+4) gives the number of solutions m where 0 < m < 2^n and A014682^n(m) < 3 and A014682^n(m+2^n) = A014682^n(m)+9. - Thomas Scheuerle, Apr 25 2021

Links

Table of n, a(n) for n=0..55.

Kival Ngaokrajang, Illustration of initial terms, Continuously concatenate pattern

Formula

Empirical g.f.: x^7 / ((1-x)^3*(1-x+x^2)*(1+x+x^2)). - Colin Barker, Jan 31 2016

Prog

(PARI) a = 3; d1 = 2; print1("0, 0, 0, 0, 0, 0, 0, 1, 3, ");
for (n = 3, 100, d2 = 0; if (Mod(n, 6)==1 || Mod(n, 6)==2, d2 = 1); d1 = d1 + d2; a = a + d1; print1(a, ", "))

Crossrefs

Cf. A112421, A267489, A014682.

Sequence in context: A279539 A174059 A321676 * A240992 A165704 A275852

Adjacent sequences: A268289 A268290 A268291 * A268293 A268294 A268295

Keyword

base,nonn

Author

Kival Ngaokrajang, Jan 31 2016

Status

approved