A244730 a(n) = 2*n^4.

0, 2, 32, 162, 512, 1250, 2592, 4802, 8192, 13122, 20000, 29282, 41472, 57122, 76832, 101250, 131072, 167042, 209952, 260642, 320000, 388962, 468512, 559682, 663552, 781250, 913952, 1062882, 1229312, 1414562, 1620000, 1847042, 2097152, 2371842, 2672672

Offset: 0

Author

Vincenzo Librandi, Jul 05 2014

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A000583, A141046, A219056.

Programs

Magma

[2*n^4: n in [0..40]];

Magma

I:=[0,2,32,162, 512]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..40]];

Mathematica

Table[2 n^4, {n, 0, 40}] (* or *) CoefficientList[Series[2(x + 11 x^2 + 11 x^3 + x^4)/(1 - x)^5, {x, 0, 40}], x]
LinearRecurrence[{5,-10,10,-5,1},{0,2,32,162,512},40] (* Harvey P. Dale, Jun 17 2022 *)

Formula

G.f.: 2*(x + 11*x^2 + 11*x^3 + x^4)/(1 - x)^5.

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n>4.

a(n) = (A082044(n) + A099761(n+1)-2)/2. - Bruce J. Nicholson, Jun 12 2017