

A027656


Expansion of 1/(1x^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
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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/(1x^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: A234584 A234585 A257770 * A142150 A276457 A171181
Adjacent sequences: A027653 A027654 A027655 * A027657 A027658 A027659


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



