proposed

approved

editing

proposed

Number of integer pairs (x,y) with x+y < 3*n/4, x-y < 3*n/4 and -x/2 < y < 2*x.

G.f.: -x^2*(x^2 - x + 1)*(x^5 + x^4 + x^3 + 2*x^2 + 3*x + 1) / ( (1+x)^2*(x^2+1)^2*(x-1)^3 ).

proposed

editing

editing

proposed

Number of integer pairs (x,y) with x+y<3n3*n/4, x-y<3n3*n/4 and -x/2<y<2x2*x.

The Comtet formula for I(n) = round(9*n^2+18-n*b(n)/16) with b(n)=bar(7,4,1,10) with period 4 , is missing divisors (32?) somewhere.

The 3 solutions for n=3 or n=4 are (x,y)=(1,0), (1,1), (2,0).

A2 A321986 := proc(n)

-11*n +35/2 +9*n^2 +9/2*(-1)^n -3*(-1)^n*n +22*A056594(n) -2*A056594(n-1) +12*(-1)^A008619(n)*A008619(n) ;

seq(AA321986(n), n=0..30) ;

allocated for R. J. Mathar

Number of integer pairs (x,y) with x+y<3n/4, x-y<3n/4 and -x/2<y<2x

0, 0, 1, 3, 3, 5, 9, 14, 14, 19, 26, 34, 34, 42, 52, 63, 63, 74, 87, 101, 101, 115, 131, 148, 148, 165, 184, 204, 204, 224, 246, 269, 269, 292, 317, 343, 343, 369, 397, 426, 426

0,4

The Comtet formula for I(n) = round(9*n^2+18-n*b(n)/16) with b(n)=bar(7,4,1,10) with period 4 is missing divisors (32?) somewhere.

L. Comtet, Advanced Combinatorics (Reidel, 1974), page 122, exercise 19 sequence (2).

<a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).

G.f.: -x^2*(x^2-x+1)*(x^5+x^4+x^3+2*x^2+3*x+1) / ( (1+x)^2*(x^2+1)^2*(x-1)^3 ).

A056594 := proc(n)

if type (n, 'odd') then

0;

else

(-1)^(n/2) ;

end if;

end proc:

A008619 := proc(n)

1+iquo(n, 2) ;

end proc:

A2 := proc(n)

if n =0 then

0;

else

-11*n+35/2+9*n^2+9/2*(-1)^n-3*(-1)^n*n+22*A056594(n)-2*A056594(n-1)+12*(-1)^A008619(n)*A008619(n) ;

%/32 ;

end if;

end proc:

seq(A(n), n=0..30) ;

allocated

nonn,easy,less

R. J. Mathar, Nov 23 2018

approved

editing

allocated for R. J. Mathar

allocated

approved