A109247 -id:A109247 - cp's OEIS frontend

A109265 Row sums of Riordan array (1-x-x^2,x(1-x)).

1, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0, 2, 2, 0, -2, -2, 0

Offset: 0

Paul Barry, Jun 24 2005

			G.f. = 1 - 2*x^2 - 2*x^3 + 2*x^5 + 2*x^6 - 2*x^8 - 2*x^9 + 2*x^11 + 2*x^12 + ...

G. C. Greubel, Table of n, a(n) for n = 0..2500
Index entries for linear recurrences with constant coefficients, signature (1,-1).

Cf. A006355, A109247, A130772, A184334, A257076.

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x-x^2)/(1-x+x^2))); // G. C. Greubel, Aug 04 2018

CoefficientList[Series[(1-x-x^2)/(1-x+x^2), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2018 *)
LinearRecurrence[{1,-1},{1,0,-2},120] (* Harvey P. Dale, Apr 08 2019 *)

{a(n) = n+=2; if( n<3, n==2, 2 * (n%3>0) * (-1)^(n\3))}; /* Michael Somos, Apr 15 2015 */

G.f.: (1-x-x^2)/(1-x+x^2).
a(n) = -a(n+3) if n>0. - Michael Somos, Apr 15 2015
a(n) = A257076(n+1). - Michael Somos, Apr 15 2015
Convolution inverse of A006355. - Michael Somos, Apr 15 2015
a(n) = A130772(n+1) = A184334(n+2) if n>0. - Michael Somos, Sep 01 2015

A132380 Period 8: repeat [0, 0, 1, 1, 0, 0, -1, -1].

Original entry on oeis.org

0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1

Offset: 0

Paul Curtz, Nov 10 2007

Antti Karttunen, Table of n, a(n) for n = 0..8191
Index entries for linear recurrences with constant coefficients, signature (0,0,0,-1).

Cf. A109247.

PadRight[{},120,{0,0,1,1,0,0,-1,-1}] (* Harvey P. Dale, Mar 17 2016 *)

a(n)=[0,0,1,1,0,0,-1,-1][n%8+1] \\ Charles R Greathouse IV, Jun 02 2011

(define (A132380 n) (list-ref '(0 0 1 1 0 0 -1 -1) (modulo n 8))) ;; Antti Karttunen, Aug 12 2017

O.g.f.: x^2*(1+x)/(1+x^4). - R. J. Mathar, Apr 06 2008
For n > 0, a(n) = A109247(n)/-3. - Antti Karttunen, Aug 12 2017
a(n) = (1/2)*(1-(-1)^floor(n/2))*(-1)^floor(n/4). - Wesley Ivan Hurt, Aug 31 2019

A109246 Riordan array (1-x-2x^2,x(1-x)).

Original entry on oeis.org

1, -1, 1, -2, -2, 1, 0, -1, -3, 1, 0, 2, 1, -4, 1, 0, 0, 3, 4, -5, 1, 0, 0, -2, 2, 8, -6, 1, 0, 0, 0, -5, -2, 13, -7, 1, 0, 0, 0, 2, -7, -10, 19, -8, 1, 0, 0, 0, 0, 7, -5, -23, 26, -9, 1, 0, 0, 0, 0, -2, 14, 5, -42, 34, -10, 1, 0, 0, 0, 0, 0, -9, 19, 28, -68, 43, -11, 1, 0, 0, 0, 0, 0, 2, -23, 14, 70, -102, 53, -12, 1, 0, 0, 0, 0, 0, 0, 11, -42, -14

Offset: 0

Paul Barry, Jun 23 2005

Matrix inverse of A109244. Row sums are A109247. Diagonal sums are A109248.

			Rows begin
1;
-1,1;
-2,-2,1;
0,-1,-3,1;
0,2,1,-4,1;
0,0,3,4,-5,1

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A109265 Row sums of Riordan array (1-x-x^2,x(1-x)).

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A132380 Period 8: repeat [0, 0, 1, 1, 0, 0, -1, -1].

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A109246 Riordan array (1-x-2x^2,x(1-x)).

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