OFFSET
0
COMMENTS
The binomial transform is 1, 1, 1, 2, 5, 12, 27,..., i.e., A000325 with another 1 in front. The inverse binomial transform is 1, -1, 1, 0, -3, 10, -25, 56, -119, 246, -501, 1012,... essentially A000247. R. J. Mathar, Feb 16 2023
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
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for linear recurrences with constant coefficients, signature (0, 1).
FORMULA
G.f.: (-1 + x^2 - x^3)/(-1 + x^2). - Michael De Vlieger, Dec 21 2015
EXAMPLE
From Michael De Vlieger, Dec 21 2015: (Start)
First 8 rows at right, the center column values in parentheses are the values of the terms of this sequence at left:
a(1) (1)
a(2) 1 (0) 0
a(3) 0 0 (0) 1 0
a(4) 1 1 1 (1) 0 0 1
a(5) 0 0 0 0 (0) 0 1 0 0
a(6) 1 1 1 1 1 (1) 1 0 0 1 1
a(7) 0 0 0 0 0 0 (0) 0 0 1 0 0 0
a(8) 1 1 1 1 1 1 1 (1) 1 1 0 0 1 1 1
(End)
MATHEMATICA
Table[SeriesCoefficient[(-1 + x^2 - x^3)/(-1 + x^2), {x, 0, n}], {n, 0, 120}] (* Michael De Vlieger, Dec 21 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert Price, Dec 20 2015
STATUS
approved