login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052460 3-magic series constant. 3
1, 50, 675, 4624, 21125, 73926, 214375, 540800, 1225449, 2550250, 4952651, 9082800, 15873325, 26622974, 43095375, 67634176, 103295825, 154001250, 224707699, 321602000, 452316501, 626168950, 854427575, 1150602624 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)