

A268292


a(n) is the total number of isolated 1's at the boundary between nth and (n1)th iterations in the pattern of A267489.


1



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
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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 nth and (n1)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 / ((1x)^3*(1x+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



