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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 (list; graph; refs; listen; history; text; internal format)
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

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: A278347 A120936 A214438 * A101675 A051764 A268533

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

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)