0,3

Number of choices for nonnegative integers x,y,z such that x and y are even and x+y+z=n.

a(n) = number of partitions of n+4 such that the differences between greatest and smallest parts are 2: a(n-4)=A097364(n,2) for n>3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 09 2004

a(n) = A108299(n-2,n)*(-1)^floor((n+1)/2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005

H. D. Brunk, An Introduction to Mathematical Statistics, Ginn, Boston, 1960; p. 360.

Index entries for two-way infinite sequences

a(n)=(2n+5)(-1)^n/16+(2n^2+10n+11)/16; a(n)=sum{k=0..n, ((k+2)(1+(-1)^k))/4 }. - Paul Barry (pbarry(AT)wit.ie), May 31 2003

G.f.: 1/((1-x)(1-x^2)^2). E.g.f.: exp(x)(2x^2+12x+11)/16+exp(-x)(-2x+5)/16. a(-n)=a(-5+n).

a(n)=sum{k=0..n, floor((k+2)/2)(1-(-1)^(n+k-1))/2}; a(n)=sum{k=0..floor(n/2), floor((n-2k+2)/2)}; - Paul Barry (pbarry(AT)wit.ie), Apr 16 2005

A signed version of A008805 is given by sum{k=0..n, (-1)^k floor(k^2/4)}. - Paul Barry (pbarry(AT)wit.ie), Aug 19 2003

a(n+1)=[sum{k=1..n, k} mod (n+1)] + a(n), with n>=1 and a(1)=1 - Paolo P. Lava (ppl(AT)spl.at), Mar 19 2007

1/((1-x)*(1-x^2)^2);

a:=n->sum(j, j=0..n/2): seq(a(n), n=2..50); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007

(PARI) a(n)=(n\2+2)*(n\2+1)/2

Diagonal sums of A002260, when arranged as a number triangle. - Paul Barry (pbarry(AT)wit.ie), Feb 28 2003

Sequence in context: A110261 A049318 A079551 this_sequence A026925 A088528 A131942

Adjacent sequences: A008802 A008803 A008804 this_sequence A008806 A008807 A008808

nonn

N. J. A. Sloane (njas(AT)research.att.com).