A306105 Numbers with digits in {0,1,2} such that every other digit is strictly less than its neighbors.

0, 1, 2, 10, 20, 21, 101, 102, 201, 202, 212, 1010, 1020, 1021, 2010, 2020, 2021, 2120, 2121, 10101, 10102, 10201, 10202, 10212, 20101, 20102, 20201, 20202, 20212, 21201, 21202, 21212, 101010, 101020, 101021, 102010, 102020, 102021, 102120, 102121

Offset: 1

Author

M. F. Hasler, Oct 05 2018

Keywords

• nonn
• base

Comments

Terms of A032858 written in base 3.

There are A000045(n+2) terms with n digits (where 0 is taken to have no digits), so the first term with n digits is at index A000071(n+3). See A032858 for the proof.

Crossrefs

Cf. A306106 .. A306111 and A297147: analog for bases 3..9 and 10.

Cf. A000045 (Fibonacci), A000071(n) = Sum(k=0..n-2,A45(k)) = A000045(n)-1.

Cf. A032858 and A032859 .. A032865 for other bases 3..10.

Programs

PARI

{A=[0,1,2]; F=[1,1]; for(n=0,4, F=[F[2],vecsum(F)]; for(k=1,3, T=max(k*10,21)*10^n; A=concat(A,apply(t->t+T,A[F[2]-1+if(k>2,F*[2,-1]~)..vecsum(F)-2]))));A}

Formula

a(n) = A007089(A032858(n)).