A139488 Binomial transform of [1, 2, 3, 4, 0, 0, 0, ...].

1, 3, 8, 20, 43, 81, 138, 218, 325, 463, 636, 848, 1103, 1405, 1758, 2166, 2633, 3163, 3760, 4428, 5171, 5993, 6898, 7890, 8973, 10151, 11428, 12808, 14295, 15893, 17606, 19438, 21393, 23475, 25688, 28036, 30523, 33153, 35930, 38858, 41941, 45183

Offset: 0

Author

Gary W. Adamson, Apr 23 2008

Keywords

• nonn
• easy

Examples

			a(5) = 43 = (1, 4, 6, 4, 1) dot (1, 2, 3, 4, 0) = (1 + 8, + 18 + 16 + 0).
		

Crossrefs

Cf. A005408, A007318, A104249, A116445.

Programs

Maple

a:=proc(n) options operator, arrow: (2/3)*n^3-(1/2)*n^2+(11/6)*n+1 end proc: seq(a(n),n=0..35); # Emeric Deutsch, Apr 30 2008

Mathematica

f[n_] := Plus @@ (Table[ Binomial[n - 1, i], {i, 0, n - 1}] PadRight[{1, 2, 3, 4}, n]); Array[f, 43] (* Robert G. Wilson v, Apr 24 2008 *)

Formula

Equals A007318 * [1, 2, 3, 4, 0, 0, 0, ...].

a(n) = (4n^3 - 3n^2 + 11n + 6)/6. - Emeric Deutsch, Apr 30 2008

G.f.: (1 - x + 2*x^2 + 2*x^3)/(1-x)^4. - Colin Barker, Feb 01 2012

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Apr 24 2008