OFFSET
1,2
COMMENTS
The original name was: Number of "ON" cells at n-th stage in a cellular automaton (or pseudo cellular automaton) related to sigma (see Comments for precise definition).
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10075 (rows n = 1..500, flattened)
Hartmut F. W. Hoft, Proof that right border of triangle is A024916
FORMULA
From Hartmut F. W. Hoft, Apr 30 2024: (Start)
EXAMPLE
Triangle begins:
1;
4;
9, 8;
16, 15;
25, 21;
36, 32, 33;
49, 40, 41;
64, 55, 56;
81, 65, 69;
100, 84, 88, 87;
121, 96, 100, 99;
144, 119, 128, 127;
169, 133, 142, 141;
196, 160, 169, 165;
225, 176, 192, 188, 189;
256, 207, 223, 219, 220;
289, 225, 241, 237, 238;
...
From Omar E. Pol, Apr 20 2024: (Start)
Illustration of the 6th row as the area of a polygon (or the number of cells) in the fourth quadrant:
. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
. | | | | | |
. | | | | | |
. | | | | | |
. | | | _ _| | _|
. | | | | | _|
. |_ _ _ _ _ _| |_ _ _ _| |_ _ _ _|
.
. 36 36 - 4 = 32 36 - 4 + 1 = 33
.
(End)
MATHEMATICA
Map[Accumulate, Table[(-2 Boole[EvenQ[k]] + 1)*Ceiling[(n + 1)/k - (k + 1)/2]^2, {n, 20}, {k, Floor[(Sqrt[8*n + 1] - 1)/2]}]] // Flatten (* Michael De Vlieger, Apr 30 2024, after Hartmut F. W. Hoft at A235791 *)
CROSSREFS
Row n has length A003056(n).
The first element of column k is in row A000217(k).
Column 1 gives the positive terms of A000290.
Right border gives A024916.
Row n is the alternating sum of entries in row n of A236104.
KEYWORD
nonn,tabf
AUTHOR
Omar E. Pol, Jan 29 2014
EXTENSIONS
New name from Hartmut F. W. Hoft, Apr 27 2024
0 removed, offset changed and minor edits from Omar E. Pol, Apr 28 2024
STATUS
approved