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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 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.)