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A321986 Number of integer pairs (x,y) with x+y < 3*n/4, x-y < 3*n/4 and -x/2 < y < 2*x. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..40.

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

FORMULA

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 ).

EXAMPLE

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

MAPLE

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:

A321986 := 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(A321986(n), n=0..30) ;

CROSSREFS

Sequence in context: A245143 A325849 A104220 * A325187 A209083 A137202

Adjacent sequences:  A321983 A321984 A321985 * A321987 A321988 A321989

KEYWORD

nonn,easy,less

AUTHOR

R. J. Mathar, Nov 23 2018

STATUS

approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)