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A306111 Numbers with digits in {0,...,8} such that every other digit is strictly less than its neighbors.

%I A306111 #6 Oct 12 2018 00:51:12
%S A306111 0,1,2,3,4,5,6,7,8,10,20,21,30,31,32,40,41,42,43,50,51,52,53,54,60,61,
%T A306111 62,63,64,65,70,71,72,73,74,75,76,80,81,82,83,84,85,86,87,101,102,103,
%U A306111 104,105,106,107,108,201,202,203,204,205,206,207,208,212,213,214,215,216,217,218,301,302,303,304,305,306,307
%N A306111 Numbers with digits in {0,...,8} such that every other digit is strictly less than its neighbors.
%C A306111 Terms of A032864 written in base 9.
%F A306111 a(n) = A007095(A032864(n)).
%F A306111 Numbers in A297147 having no digit 9: Intersection of A297147 with A007095.
%e A306111 There are 1+2+3+4+5+6+7+8 = 9*4 = 36 terms with 2 digits.
%e A306111 We obtain the 3-digit terms by appending to each of these the 1-digit terms starting with a digit larger than the last digit of the prefix: 10.{1..8}, 20.{1..8}, 21.{2..8}, 30.{1..8}, ..., 86.{7..8}, 87.{8}.
%e A306111 We obtain the 4-digit terms by appending to each of the 2 digit terms, the 2-digit terms starting with a digit larger than the last digit of the prefix: 10.{10,...,87}, 20.{10,...,87}, 21.{20,...,87}, 30.{10,...,87}, ..., 86.{70,...,87}, 87.{80..87}.
%e A306111 That way we obtain all terms with n digits by taking the 2-digit terms and appending to each of these the suitable subsequence of n-2 digit terms.
%o A306111 (PARI) A(Nmax=100,K=8,A=[0..K],i=vector(2*K,i,max(1,i-K+1)),c(T,v)=apply(t->t+T,v))={for(n=0,oo, for(k=10,K*11-1,if(k%10<k\10, k%10|| i=concat(i,1+#A); A=concat(A,c(k*10^n,A[i[K*n+k%10+1]..i[K*n+K+1]-1])); #A<Nmax||return(A))))}
%Y A306111 Cf. A306105 .. A306110 and A297147: analog for bases 3..8 and 10.
%Y A306111 Cf. A032864 and A032858 .. A032865 for other bases 3..10.
%K A306111 nonn,base
%O A306111 1,3
%A A306111 _M. F. Hasler_, Oct 05 2018