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A173432
NW-SE diagonal sums of Riordan array A112468.
3
1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0
OFFSET
1,3
COMMENTS
Matches Fibonacci-sequence, such that F(n) + a(n) and F(n) - a(n) = always even.
Periodic sequence with period: [1,1,2,1,1,0]. - Philippe Deléham, Oct 11 2011
FORMULA
a(n) = 1 + A131531(n) with inverse binomial transform: 1, 0, 1, -3, 6, -11, 21, .., a signed variant of A024495. - R. J. Mathar, Mar 04 2010
a(2n+1) = a(2n)-a(2n-1)+2, a(2n) = a(2n-1)-a(2n-2) with a(1) = a(2)=1. - Philippe Deléham, Oct 11 2011
a(n) = a(n-1)-a(n-3)+a(n-4). - Colin Barker, Sep 26 2014
G.f.: -x*(x^2+1) / ((x-1)*(x+1)*(x^2-x+1)). - Colin Barker, Sep 26 2014
a(n) = 2*ceiling(n/6)-2*floor(n/6)+floor(n/3)-ceiling(n/3). - Wesley Ivan Hurt, Sep 27 2014
a(n) = A001045(n) - A111927(n). - Paul Curtz, Dec 16 2020
MAPLE
A173432:=n->2*ceil(n/6)-2*floor(n/6)+floor(n/3)-ceil(n/3): seq(A173432(n), n=1..100); # Wesley Ivan Hurt, Sep 27 2014
MATHEMATICA
Table[2 Ceiling[n/6] - 2 Floor[n/6] + Floor[n/3] - Ceiling[n/3], {n, 50}] (* Wesley Ivan Hurt, Sep 27 2014 *)
PROG
(PARI) Vec(-x*(x^2+1) / ((x-1)*(x+1)*(x^2-x+1)) + O(x^100)) \\ Colin Barker, Sep 26 2014
(Magma) [2*Ceiling(n/6)-2*Floor(n/6)+Floor(n/3)-Ceiling(n/3) : n in [1..100]]; // Wesley Ivan Hurt, Sep 27 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Mark Dols, Feb 18 2010
EXTENSIONS
Corrected and extended by Philippe Deléham, Oct 11 2011
STATUS
approved