OFFSET
0,2
COMMENTS
Take the first 2n positive integers and choose n of them such that their sum: a) is divisible by n, and b) is minimal. It seems their sum equals a(n). - Ivan N. Ianakiev, Feb 16 2019
REFERENCES
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.
LINKS
Robert Price, Table of n, a(n) for n = 0..999
Emanuele Munarini, Topological indices for the antiregular graphs, Le Mathematiche (2021) Vol. 76, No. 1, see p. 301.
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
FORMULA
Conjectures from Colin Barker, Dec 08 2015 and Apr 20 2019: (Start)
a(n) = (n+1)*(2*n -(-1)^n +5)/4.
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4.
G.f.: (1+3*x) / ((1-x)^3*(1+x)^2).
(End)
a(n) = n + 1 + (n+1) * floor((n+1)/2), conjectured. - Wesley Ivan Hurt, Dec 25 2016
a(n) = A093353(n) + n + 1, conjectured. - Matej Veselovac, Jan 21 2020
EXAMPLE
From Michael De Vlieger, Dec 14 2015: (Start)
First 12 rows, replacing "0" with "." for better visibility of ON cells, followed by the total number of 1's per row, and the running total up to that row:
1 = 1 -> 1
1 1 1 = 3 -> 4
1 . . . 1 = 2 -> 6
1 1 1 . 1 1 1 = 6 -> 12
1 . . . 1 . . . 1 = 3 -> 15
1 1 1 . 1 1 1 . 1 1 1 = 9 -> 24
1 . . . 1 . . . 1 . . . 1 = 4 -> 28
1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 = 12 -> 40
1 . . . 1 . . . 1 . . . 1 . . . 1 = 5 -> 45
1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 = 15 -> 60
1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 = 6 -> 66
1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 . 1 1 1 = 18 -> 84
1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 . . . 1 = 7 -> 91
(End)
MAPLE
MATHEMATICA
rule = 54; rows = 30; Table[Total[Take[Table[Total[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}], k]], {k, 1, rows}]
Accumulate[Total /@ CellularAutomaton[54, {{1}, 0}, 52]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 05 2015
STATUS
approved