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A099627 Triangle read by rows: T(n,k)=2^n+2^k-1 with n>=k>=0. 13
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, 79, 95, 127, 128, 129, 131, 135, 143, 159, 191, 255, 256, 257, 259, 263, 271, 287, 319, 383, 511, 512, 513, 515, 519, 527, 543, 575, 639, 767, 1023, 1024, 1025, 1027, 1031, 1039 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
Numbers in A000225 or A099628.
LINKS
FORMULA
As sequence, a(n)=A048645(n+2)-1.
EXAMPLE
Triangle starts: In binary:
k = 0 1 2 3 4 5
n
0 1 1
1 2 3 10 11
2 4 5 7 100 101 111
3 8 9 11 15 1000 1001 1011 1111
4 16 17 19 23 31 10000 10001 10011 10111 11111
5 32 33 35 39 47 63 100000 100001 100011 100111 101111 111111
E.g. T(5,3) = 2^5 + 2^3-1 = 32 + 7 = 39 (100111 in binary).
MATHEMATICA
Table[2^n+2^k -1, {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 27 2016 *)
PROG
(Haskell)
a099627 n k = a099627_tabl !! n !! k
a099627_row n = a099627_tabl !! n
a099627_tabl = iterate (\xs@(x:_) -> (2 * x) : map ((+ 1) . (* 2)) xs) [1]
-- Reinhard Zumkeller, Dec 19 2012
CROSSREFS
A053221 (row sums), A000079 (left diagonal), A000225 (right diagonal).
A048645 (see formula).
Partial sums of A232089.
Sequence in context: A140691 A328668 A316468 * A324841 A184155 A331913
KEYWORD
easy,nonn,tabl
AUTHOR
Henry Bottomley, Oct 25 2004
STATUS
approved

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Last modified March 29 06:15 EDT 2024. Contains 371265 sequences. (Running on oeis4.)