|
|
A097065
|
|
Interleave n+1 and n-1.
|
|
7
|
|
|
1, -1, 2, 0, 3, 1, 4, 2, 5, 3, 6, 4, 7, 5, 8, 6, 9, 7, 10, 8, 11, 9, 12, 10, 13, 11, 14, 12, 15, 13, 16, 14, 17, 15, 18, 16, 19, 17, 20, 18, 21, 19, 22, 20, 23, 21, 24, 22, 25, 23, 26, 24, 27, 25, 28, 26, 29, 27, 30, 28, 31, 29, 32, 30, 33, 31, 34, 32, 35, 33, 36, 34, 37, 35, 38
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Pairwise sums are abs(A023443), or n - 1 + 2*0^n. The partial sums of this sequence is A000124, with extra leading 1. Partial sums are A097066. Binomial transform is A097067.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1 - 2*x + 2*x^2)/((1 + x)*(1 - x)^2).
a(n) = (2*n - 1)/4 + 5*(-1)^n/4.
E.g.f.: ((2 + x)*cosh(x) - (3 - x)*sinh(x))/2. - Stefano Spezia, Jul 01 2023
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[(2n - 1)/4 + 5(-1)^n/4, {n, 0, 75}] (* Or *) Flatten[ Table[{n + 1, n - 1}, {n, 0, 37}]] (* Or *) CoefficientList[Series[(1 - 2x + 2x^2)/((1 + x)(1 - x)^2), {x, 0, 75}], x] (* Robert G. Wilson v, Jul 24 2004 *)
|
|
PROG
|
(Haskell)
import Data.List (transpose)
a097065 n = n' - 2 * m where (n', m) = divMod (n + 2) 2
a097065_list = concat $ transpose [[1 ..], [-1 ..]]
(Magma) [(2*n-1)/4 + 5*(-1)^n/4 : n in [0..100]]; // Wesley Ivan Hurt, Jan 10 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|