A052459 a(n) = n*(2*n^2 + 1)*(n^2 + 1)/6.

1, 15, 95, 374, 1105, 2701, 5775, 11180, 20049, 33835, 54351, 83810, 124865, 180649, 254815, 351576, 475745, 632775, 828799, 1070670, 1366001, 1723205, 2151535, 2661124, 3263025, 3969251, 4792815, 5747770, 6849249, 8113505

Offset

1,2

Comments

2-magic series constant.

Links

G. C. Greubel, 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 (6,-15,20,-15,6,-1).

Formula

G.f.: x*(1 + 3*x + x^2)*(1 + 6*x + x^2)/(1-x)^6. - Chai Wah Wu, Dec 17 2016

E.g.f.: x*(6 +39*x +53*x^2 +20*x^3 +2*x^4)*exp(x)/6. - G. C. Greubel, Sep 23 2019

Maple

seq(n*(2*n^2 +1)*(n^2 +1)/6, n=1..30); # G. C. Greubel, Sep 23 2019

Mathematica

Table[n*(2*n^2 +1)*(n^2 +1)/6, {n, 30}] (* G. C. Greubel, Sep 23 2019 *)

Prog

(PARI) vector(30, n, n*(2*n^2 +1)*(n^2 +1)/6) \\ G. C. Greubel, Sep 23 2019
(Magma) [n*(2*n^2 +1)*(n^2 +1)/6: n in [1..30]]; // G. C. Greubel, Sep 23 2019
(Sage) [n*(2*n^2 +1)*(n^2 +1)/6 for n in (1..30)] # G. C. Greubel, Sep 23 2019
(GAP) List([1..30], n-> n*(2*n^2 +1)*(n^2 +1)/6); # G. C. Greubel, Sep 23 2019

Crossrefs

Cf. A052460, A052461.

Sequence in context: A114240 A189657 A190274 * A336278 A044266 A044647

Adjacent sequences: A052456 A052457 A052458 * A052460 A052461 A052462

Keyword

nonn,easy

Author

Eric W. Weisstein

Extensions

Formula from Vladeta Jovovic, Jun 15 2002

Status

approved