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%I #24 Jun 26 2022 17:31:06
%S 1,2,3,4,5,7,8,9,11,15,16,17,19,23,31,32,33,35,39,47,63,64,65,67,71,
%T 79,95,127,128,129,131,135,143,159,191,255,256,257,259,263,271,287,
%U 319,383,511,512,513,515,519,527,543,575,639,767,1023,1024,1025,1027,1031,1039
%N Triangle read by rows: T(n,k)=2^n+2^k-1 with n>=k>=0.
%C Positive integers m where m-th Catalan number A000108(m)=C(2m,m)/(m+1) is not divisible by 4, i.e. where A048881(m) is 0 or 1.
%C Numbers in A000225 or A099628.
%H Reinhard Zumkeller, <a href="/A099627/b099627.txt">Rows n = 0..100 of triangle, flattened</a>
%F As sequence, a(n)=A048645(n+2)-1.
%e Triangle starts: In binary:
%e k = 0 1 2 3 4 5
%e n
%e 0 1 1
%e 1 2 3 10 11
%e 2 4 5 7 100 101 111
%e 3 8 9 11 15 1000 1001 1011 1111
%e 4 16 17 19 23 31 10000 10001 10011 10111 11111
%e 5 32 33 35 39 47 63 100000 100001 100011 100111 101111 111111
%e E.g. T(5,3) = 2^5 + 2^3-1 = 32 + 7 = 39 (100111 in binary).
%t Table[2^n+2^k -1,{n,0,10},{k,0,n}]//Flatten (* _Harvey P. Dale_, Mar 27 2016 *)
%o (Haskell)
%o a099627 n k = a099627_tabl !! n !! k
%o a099627_row n = a099627_tabl !! n
%o a099627_tabl = iterate (\xs@(x:_) -> (2 * x) : map ((+ 1) . (* 2)) xs) [1]
%o -- _Reinhard Zumkeller_, Dec 19 2012
%Y A053221 (row sums), A000079 (left diagonal), A000225 (right diagonal).
%Y A048645 (see formula).
%Y Partial sums of A232089.
%K easy,nonn,tabl
%O 0,2
%A _Henry Bottomley_, Oct 25 2004
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