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C(n-1, 4)+C(n-1, 3)+ ... +C(n-1, 0) = C(n, 4)+C(n, 2)+1 = C(n, 4)+C(n-1, 2)+n.

a(n) = Sum_{0 <= k <= 2} C(n, 2k) - Joel Sanderi (sanderi(AT)itstud.chalmers.se), Sep 08 2004

(n^4-6n^3+23n^2-18n+24)/24.

A000127 := n->1/24*n^4-1/4*n^3+23/24*n^2-3/4*n+1;

A000127 := n->(n^4 - 6*n^3 + 23*n^2 - 18*n + 24)/24;

A000127:=-(1-3*z+4*z**2-2*z**3+z**4)/(z-1)**5; [S. Plouffe in his 1992 dissertation.]

with (combstruct):ZL:=[S, {S=Sequence(U, card<r), U=Set(Z, card>=1)}, unlabeled]: seq(count(subs(r=6, ZL), size=m), m=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2008

seq(sum(binomial(n, m), m=1..4)+1, n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 17 2008

f[n_] := Sum[Binomial[n, i], {i, 0, 4}]; Table[f@n, {n, 0, 40}] (* Robert G. Wilson v (rgwv@rgwv.com), Jun 29 2007 *)

Sequence in context: A054016 A051039 A056183 this_sequence A133552 A000128 A106399

Adjacent sequences: A000124 A000125 A000126 this_sequence A000128 A000129 A000130

nonn,easy,nice

njas

Formula corrected and additional references from TORSTEN.SILLKE(AT)LHSYSTEMS.COM.

Additional correction from Jonas Paulson (jonasso(AT)sdf.lonestar.org), Oct 30 2003