来自在线整数百科全书的问候语!http://oeis.org/ Search: id:a008731 Showing 1-1 of 1 %I A008731 %S A008731 1,0,2,1,3,2,5,3,7,5,9,7,12,9,15,12,18,15,22,18,26,22,30,26,35,30,40, %T A008731 35,45,40,51,45,57,51,63,57,70,63,77,70,84,77,92,84,100,92,108,100, %U A008731 117,108,126,117,135,126,145,135,155,145,165,155,176,165,187 %N A008731 Molien series for 3-dimensional group [2, n] = *22n. %C A008731 a(n+4) is the number of solutions to the equation X + Y + Z = n such that X < Z, Y < Z, and X + Y >= Z. - _Geoffrey Critzer_, Jul 13 2013 %C A008731 Number of partitions of n into two sorts of 2, and one sort of 3. 7月14日,2013岁的G. C. Greubel,n,a(n)n=0…1000的表%H A000 831 iRIA算法项目组合结构百科全书222%H A000 831莫里恩系列索引条目%H A000 831常系数线性递归的索引项签名(0,2,1,1,-2,0,1).0%F A000 83G.F.:1(/(1-x ^ 2)^ 2 *(1-x ^ 3)).%F A000 831 A(n)=(1/48)*(2×n ^ 2 + 14 *n+27 +(6×n+21)*(-1)^ n-(n=1,mod))。2015πF A000 831 f(n)=A(-7 N),在Z-α-迈克尔索莫斯中的所有n,FEB 02 2015πF A000 831 0=A(n)+A(n+1)-A(n+2)-2*a(n+3)-a(n+4)+a(n+5)+a(n+6)-z,n=n-偶,(n+-)/^,n(n)=α(n+)-a(n+)-a(n+)-a(n+)-a(n+)-a(n+)-a(n+)-a(n+)-a(n+)-a(n+)。-迈克尔索莫斯,FEB 02-迈克尔索莫斯,FEB 02 2015 2015 %E A000 831 A(4)=3,因为我们有:%E E A000 831 1 + 3 + 4=2 + 2 + 4=3 + 1 + 1。7月13日,2013 GeFray-CrITZeLi,7月13日,E.A000 831 G.F.=1+2×x ^ 2+X^ 3+3×X ^ 4+2×X ^ 5+5×X ^ 6+3×x ^ ^++××^+××^ ^+…70); # modified by _G. C. Greubel_, Jul 30 2019 %t A008731 CoefficientList[Series[1/(1-x^2)^2/(1-x^3),{x,0,70}],x] (* _Geoffrey Critzer_, Jul 13 2013 *) %t A008731 a[ n_] := Quotient[ (2 n^2 + If[ OddQ[n], 8 n + 6, 20 n + 48]), 70]; (* _Michael Somos_, Feb 02 2015 *) %t A008731 a[ n_] := Module[{m=n}, If[ n < 0, m=-7-n]; SeriesCoefficient[ 1 / ( (1 - x^2)^2 * (1 - x^3)), {x, 0, m}]]; (* _Michael Somos_, Feb 02 2015 *) %t A008731 LinearRecurrence[{0,2,1,-1,-2,0,1},{1,0,2,1,3,2,5},70] (* _Harvey P. Dale_, Feb 23 2018 *) %o A008731 (PARI) {a(n) = (2*n^2 + if( n%2, 8*n + 6, 20*n + 48)) \ 48}; /* _Michael Somos_, Feb 02 2015 */ %o A008731 (PARI) {a(n) = if( n<0, n=-7-n); polcoeff( 1 / ((1 - x^2)^2 * (1 - x^3)) + x * O(x^n), n)}; /* _Michael Somos_, Feb 02 2015 */ %o A008731 (MAGMA) R= PrimeSeriSrin(整数(),70);Coefficients(R)!( 1/((1-x^2)^2*(1-x^3)) )); // _G. C. Greubel_, Jul 30 2019 %o A008731 (Sage) (1/((1-x^2)^2*(1-x^3))).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 30 2019 %o A008731 (GAP) a:=[1,0,2,1,3,2,5];; for n in [8..70] do a[n]:=2*a[n-2]+a[n-3]-a[n-4]-2*a[n-5]+a[n-7]; od; a; # _G. C. Greubel_, Jul 30 2019 %Y A008731 First differences of A008763. %K A008731 nonn %O A008731 0,3 %A A008731 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE