A173432 NW-SE diagonal sums of Riordan array A112468.

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

Links

Table of n, a(n) for n=1..84.

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

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

Cf. A000045, A024495, A112468, A131531.

Sequence in context: A120936 A335294 A214438 * A101675 A348916 A051764

Adjacent sequences: A173429 A173430 A173431 * A173433 A173434 A173435

Keyword

nonn,easy

Author

Mark Dols, Feb 18 2010

Extensions

Corrected and extended by Philippe Deléham, Oct 11 2011

Status

approved