A166941 Product plus sum of four consecutive nonnegative numbers.

6, 34, 134, 378, 862, 1706, 3054, 5074, 7958, 11922, 17206, 24074, 32814, 43738, 57182, 73506, 93094, 116354, 143718, 175642, 212606, 255114, 303694, 358898, 421302, 491506, 570134, 657834, 755278, 863162, 982206, 1113154, 1256774

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Oct 24 2009

Keywords

• nonn
• easy

Comments

a(n) = (n*...*(n+3))+(n+...+(n+3)), n >= 0.

All terms are even.

Binomial transform of 2*A167858.

Examples

			a(0) = 0*1*2*3+0+1+2+3 = 0+6 = 6.
a(1) = 1*2*3*4+1+2+3+4 = 24+10 = 34.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A001477 (nonnegative integers), A167858 (3,14,36,36,12,0,0,0,...), A028387 (n+(n+1)^2), A167875, A166942, A166943.

Programs

Magma

[ &*s + &+s where s is [n..n+3]: n in [0..32] ]; // Klaus Brockhaus, Nov 14 2009

Mathematica

lst={};Do[p=(n+3)*(n+2)*(n+1)*n+(n+3)+(n+2)+(n+1)+n;AppendTo[lst,p],{n,0,5!}];lst

Formula

a(n) = n^4 + 6*n^3 + 11*n^2 + 10*n + 6. - Charles R Greathouse IV, Nov 02 2009, [corrected by Klaus Brockhaus, Nov 14 2009]

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24 for n > 3; a(0)=6, a(1)=34, a(2)=134, a(3)=378. - Klaus Brockhaus, Nov 14 2009

G.f.: 2*(3 + 2*x + 12*x^2 - 6*x^3 + x^4)/(1-x)^5. - Klaus Brockhaus, Nov 14 2009

Extensions

Edited and offset corrected by Klaus Brockhaus, Nov 14 2009