A272871 Imaginary part of (n + i)^4.

0, 0, 24, 96, 240, 480, 840, 1344, 2016, 2880, 3960, 5280, 6864, 8736, 10920, 13440, 16320, 19584, 23256, 27360, 31920, 36960, 42504, 48576, 55200, 62400, 70200, 78624, 87696, 97440, 107880, 119040, 130944, 143616, 157080, 171360, 186480, 202464, 219336

Offset: 0

Author

Colin Barker, May 08 2016

Keywords

• nonn
• easy

Examples

			a(5) = 480 because (5 + i)^4 = 476 + 480*i.
		

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A002378, A007531, A064200.

Cf. A272870.

Programs

Mathematica

Table[Im[(n + I)^4], {n, 0, 38}] (* or *)
Table[4 (n - 1) n (n + 1), {n, 0, 38}] (* or *)
CoefficientList[Series[24 x^2/(1 - x)^4, {x, 0, 38}], x] (* Michael De Vlieger, May 08 2016 *)

PARI

a(n) = 4*(n-1)*n*(n+1)

PARI

vector(50, n, n--; imag((n+I)^4))

PARI

concat(vector(2), Vec(24*x^2/(1-x)^4 + O(x^50)))

Formula

a(n) = 4*A007531(n+1).

a(n) = 4*(n-1)*n*(n+1).

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3.

G.f.: 24*x^2 / (1-x)^4.

a(n) = b(n+1)*b(n-1)-b(n)*b(n-2), where b(n) is A002378(n). - Anton Zakharov, Aug 15 2016

From Ilya Gutkovskiy, Aug 15 2016: (Start)

E.g.f.: 4*x^2*(3 + x)*exp(x).

a(n) = 24*binomial(n+1,3).

a(n) = Sum_{k=0..n} A064200(k). (End)