A056578 a(n) = 1 + 2*n + 3*n^2 + 4*n^3.

1, 10, 49, 142, 313, 586, 985, 1534, 2257, 3178, 4321, 5710, 7369, 9322, 11593, 14206, 17185, 20554, 24337, 28558, 33241, 38410, 44089, 50302, 57073, 64426, 72385, 80974, 90217, 100138, 110761, 122110, 134209, 147082, 160753, 175246, 190585, 206794, 223897, 241918

Offset: 0

Author

Henry Bottomley, Jun 29 2000

Keywords

• easy
• nonn

Examples

			For n>4 this is 4321 translated from base n to base 10.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Note: 1 + 2*x + 3*x^2 + 4*x^3 is the first derivative of 1 + x + x^2 + x^3 + x^4, i.e., A053699.

Cf. A000012, A005408, A056109, A056579.

Programs

Mathematica

f[n_]:=1+2*n+3*n^2+4*n^3; lst={}; Do[AppendTo[lst,f[n]],{n,0,5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 12 2010 *)

Formula

a(n) = (A053699(n+1) - A053699(n-1))/2 - 4*n - 1.

G.f.: (1 + 6*x + 15*x^2 + 2*x^3)/(1-x)^4. - Colin Barker, Jan 10 2012

From Elmo R. Oliveira, Apr 20 2025: (Start)

E.g.f.: exp(x)*(1 + 9*x + 15*x^2 + 4*x^3).

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

Extensions

More terms from Elmo R. Oliveira, Apr 20 2025