A098355 -id:A098355 - cp's OEIS frontend

A098354 Multiplication table of the powers of 2 read by antidiagonals.

4, 8, 8, 16, 16, 16, 32, 32, 32, 32, 64, 64, 64, 64, 64, 128, 128, 128, 128, 128, 128, 256, 256, 256, 256, 256, 256, 256, 512, 512, 512, 512, 512, 512, 512, 512, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 1024, 2048, 2048, 2048, 2048, 2048, 2048, 2048, 2048

Offset: 1

Douglas Stones (dssto1(AT)student.monash.edu.au), Sep 04 2004

			4; 8,8; 16,16,16; 32,32,32,32; ...

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index to divisibility sequences

Cf. A003991, A098355.

Table[PadRight[{},n-1,2^n],{n,2,12}]//Flatten (* Harvey P. Dale, Nov 21 2021 *)

for(n=2,9,for(i=1,n-1,print1(2^n", "))) \\ Charles R Greathouse IV, Apr 09 2012

A259653 a(0)=0, a(1)=1, a(n) = min{3 a(k) + (3^(n-k)-1)/2, k=0..(n-1)} for n>=2.

Original entry on oeis.org

0, 1, 4, 7, 16, 25, 34, 61, 88, 115, 142, 223, 304, 385, 466, 547, 790, 1033, 1276, 1519, 1762, 2005, 2734, 3463, 4192, 4921, 5650, 6379, 7108, 9295, 11482, 13669, 15856, 18043, 20230, 22417, 24604, 31165, 37726, 44287, 50848, 57409, 63970, 70531, 77092

Offset: 0

Gheorghe Coserea, Jul 02 2015

nonn

A generalization of Frame-Stewart recurrence is a(0)=0, a(1)=1, a(n)=min{q*a(k) + (q^(n-k)-1)/(q-1), k=0..(n-1)} where n>=2 and q>1. The sequence of first differences is q^A003056(n). For q=2 we have the sequence A007664. The current sequence is generated for q=3.

Gheorghe Coserea, Table of n, a(n) for n = 0..4096
Jonathan Chappelon and Akihiro Matsuura, On generalized Frame-Stewart numbers, arXiv:1009.0146 [math.NT], 2010.
P. Stockmeyer, Variations on the Four-Post Tower of Hanoi Puzzle

Cf. A003056, A007664.

Essentially partial sums of A098355.

a[n_] := a[n] = Min[ Table[ 3*a[k] + (3^(n-k) - 1)/2, {k, 0, n-1}]]; a[0] = 0; Table[a[n], {n, 0, 60}]

a(n) = min {3*a(k) + (3^(n-k)-1)/2 ; k < n}.

a(n) = sum(3^A003056(i), i=0..n-1).

cp's OEIS Frontend

A098354 Multiplication table of the powers of 2 read by antidiagonals.

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