A232089 Table read by rows, which consist of 1 followed by 2^k, 0 <= k < n ; n = 0,1,2,3,...

1, 1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 4, 8, 1, 1, 2, 4, 8, 16, 1, 1, 2, 4, 8, 16, 32, 1, 1, 2, 4, 8, 16, 32, 64, 1, 1, 2, 4, 8, 16, 32, 64, 128, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512

Offset

0,6

Comments

The n-th row consists of the n+1 terms A011782(k), k=0,...,n. Thus the rows converge to A011782, which is also equal to the diagonal = last element of each row.

This (read as a "linear" sequence) is also the limit of the rows of A232088; more precisely, for n>0, each row of A232088 consists of the first n(n+1)/2 elements of this sequence, followed by 2^(n-1). See the LINK there for one motivation for this sequence.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

T(n,k) = max(1,2^(k-1)) = A011782(k); 0 <= k <= n.

Example

The table reads:
1,
1, 1,
1, 1, 2,
1, 1, 2, 4,
1, 1, 2, 4, 8,
1, 1, 2, 4, 8, 16,
1, 1, 2, 4, 8, 16, 32,
1, 1, 2, 4, 8, 16, 32, 64, etc.

Mathematica

Join[{1}, Flatten[Table[Join[{1}, 2^Range[0, n]], {n, 0, 10}]]] (* Harvey P. Dale, Nov 28 2024 *)

Prog

(PARI) for(n=0, 10, print1("1, "); for(k=0, n-1, print1(2^k, ", ")))

Crossrefs

Sequence in context: A340191 A182105 A023506 * A141021 A140995 A140994

Adjacent sequences: A232086 A232087 A232088 * A232090 A232091 A232092

Keyword

nonn,tabl,easy

Author

M. F. Hasler, Jan 20 2014

Status

approved