A329361 a(n) = Sum_{i = 1..n} 2^(n - i) * A000002(i).

0, 1, 4, 10, 21, 43, 88, 177, 356, 714, 1429, 2860, 5722, 11445, 22891, 45784, 91569, 183139, 366280, 732562, 1465125, 2930252, 5860505, 11721011, 23442024, 46884049, 93768100, 187536202, 375072405, 750144811, 1500289624, 3000579249, 6001158499, 12002317000

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Formula

a(n + 1) = A000002(n) + 2 a(n).

Example

The first 5 terms of A000002 are {1, 2, 2, 1, 1}, so a(5) = 2^4 * 1 + 2^3 * 2 + 2^2 * 2 + 2^1 * 1 + 2^0 * 1 = 43.

Mathematica

kolagrow[q_]:=If[Length[q]<2, Take[{1, 2}, Length[q]+1], Append[q, Switch[{q[[Length[Split[q]]]], q[[-2]], Last[q]}, {1, 1, 1}, 0, {1, 1, 2}, 1, {1, 2, 1}, 2, {1, 2, 2}, 0, {2, 1, 1}, 2, {2, 1, 2}, 2, {2, 2, 1}, 1, {2, 2, 2}, 1]]]
kol[n_Integer]:=If[n==0, {}, Nest[kolagrow, {1}, n-1]];
Table[FromDigits[kol[n], 2], {n, 0, 30}]

Crossrefs

Cf. A000002, A054353, A088568, A288605, A296658, A329315, A329316, A329355, A329356, A329360, A329362.

Sequence in context: A264079 A053643 A111927 * A290998 A369846 A227803

Adjacent sequences: A329358 A329359 A329360 * A329362 A329363 A329364

Keyword

nonn

Author

Gus Wiseman, Nov 12 2019

Status

approved