A052460 3-magic series constant.

1, 50, 675, 4624, 21125, 73926, 214375, 540800, 1225449, 2550250, 4952651, 9082800, 15873325, 26622974, 43095375, 67634176, 103295825, 154001250, 224707699, 321602000, 452316501, 626168950, 854427575, 1150602624

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Magic Constant.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = n^3/4 * (n^2 + 1)^2.

G.f.: x*(1 +42*x +303*x^2 +568*x^3 +303*x^4 +42*x^5 +x^6)/(1-x)^8 .

a(1)=1, a(2)=50, a(3)=675, a(4)=4624, a(5)=21125, a(6)=73926, a(7)= 214375, a(8)=540800, a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) + 56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8). - Harvey P. Dale, Aug 14 2013

E.g.f.: x*(4 +96*x +352*x^2 +370*x^3 +142*x^4 +21*x^5 + x^6)*exp(x)/4. - G. C. Greubel, Sep 23 2019

Maple

seq(n^3*(1+n^2)^2/4, n=1..30); # G. C. Greubel, Sep 23 2019

Mathematica

Table[n^3/4 (n^2+1)^2, {n, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 50, 675, 4624, 21125, 73926, 214375, 540800}, 30] (* Harvey P. Dale, Aug 14 2013 *)
CoefficientList[Series[(1+42x+303x^2+568x^3+303x^4+42x^5+x^6)/(1-x)^8, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 14 2013 *)

Prog

(PARI) vector(30, n, n^3*(1+n^2)^2/4) \\ G. C. Greubel, Sep 23 2019
(Magma) [n^3*(1+n^2)^2/4: n in [1..30]]; // G. C. Greubel, Sep 23 2019
(Sage) [n^3*(1+n^2)^2/4 for n in (1..30)] # G. C. Greubel, Sep 23 2019
(GAP) List([1..30], n-> n^3*(1+n^2)^2/4); # G. C. Greubel, Sep 23 2019

Crossrefs

Cf. A052459, A052461.

Sequence in context: A240385 A282766 A323485 * A224168 A223859 A223982

Adjacent sequences: A052457 A052458 A052459 * A052461 A052462 A052463

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved