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A027656 Expansion of 1/(1-x^2)^2 (included only for completeness - the policy is always to omit the zeros from such sequences). 29
1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 12, 0, 13, 0, 14, 0, 15, 0, 16, 0, 17, 0, 18, 0, 19, 0, 20, 0, 21, 0, 22, 0, 23, 0, 24, 0, 25, 0, 26, 0, 27, 0, 28, 0, 29, 0, 30, 0, 31, 0, 32, 0, 33, 0, 34, 0, 35, 0, 36, 0, 37, 0, 38, 0, 39, 0, 40, 0, 41, 0, 42, 0, 43, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = (n+2)(n+3)/2 mod n+2. - Amarnath Murthy, Jun 17 2004

a(n) is the number of nonnegative integer solutions to the equation x+y+z=n such that x+y=z. - Geoffrey Critzer, Jul 12 2013

LINKS

Table of n, a(n) for n=0..85.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1)

FORMULA

From Paul Barry, May 27 2003: (Start)

Binomial transform is A045891. Partial sums are A008805. The sequence 0, 1, 0, 2, ... has a(n)=floor((n+2)/2)(1-(-1)^n)/2.

a(n) = floor((n+3)/2)(1+(-1)^n)/2. (End)

a(n) = ((1+(-1)^n)/4)*Sum_{k=0..n} (1+(-1)^k). - Paolo P. Lava, Nov 30 2007

a(n) = (n+2)*(1 + (-1)^n))/4. - Bruno Berselli, Apr 01 2011

a(n) = A008619(n) * A059841(n). - Wesley Ivan Hurt, Jun 17 2013

MATHEMATICA

nn=100; CoefficientList[Series[1/(1-x^2)^2, {x, 0, nn}], x] (* Geoffrey Critzer, Jul 12 2013 *)

PROG

(MAGMA) [(n+2)*(1+(-1)^n)/4: n in [0..75]]; // Vincenzo Librandi, Apr 02 2011

(PARI) a(n)=if(n%2, 0, n/2+1) \\ Charles R Greathouse IV, Jan 18 2012

CROSSREFS

Cf. A142150.

Sequence in context: A234585 A257770 * A142150 A276457 A171181 A034948

Adjacent sequences:  A027653 A027654 A027655 * A027657 A027658 A027659

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 15 21:06 EDT 2018. Contains 316237 sequences. (Running on oeis4.)