A121672 Real part of (n + i)^5.

0, -4, -38, -12, 404, 1900, 5646, 13412, 27688, 51804, 90050, 147796, 231612, 349388, 510454, 725700, 1007696, 1370812, 1831338, 2407604, 3120100, 3991596, 5047262, 6314788, 7824504, 9609500, 11705746, 14152212, 16990988, 20267404, 24030150

Offset

0,2

Comments

The companion sequence A121671 uses the operation (1 + n*i)^5.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: -2*x*(2+7*x-78*x^2+7*x^3+2*x^4)/(1-x)^6. - Bruno Berselli, Mar 01 2012

a(n) = n*(n^4-10*n^2+5). - Bruno Berselli, Mar 01 2012

a(n) = (1+n^2)^(5/2)*sin(5*arctan(n)). - Gerry Martens, Apr 06 2024

Example

a(4) = 404 since (4 + i)^5 = (404 + 1121i) where 1121 = A121671(4).

Mathematica

Re[(Range[0, 30]+I)^5] (* Harvey P. Dale, Mar 01 2012 *)

Prog

(PARI) a(n) = real((n + I)^5); \\ Michel Marcus, Dec 19 2020

Crossrefs

Cf. A121671, A080663, A121670.

Sequence in context: A144991 A073237 A218334 * A020205 A265437 A003633

Adjacent sequences: A121669 A121670 A121671 * A121673 A121674 A121675

Keyword

sign,easy

Author

Gary W. Adamson, Aug 14 2006

Extensions

Corrected and extended by Harvey P. Dale, Mar 01 2012

Status

approved