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

0,1

Comments

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

All terms are even.

Binomial transform of 2*A167858.

Links

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

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

Example

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.

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

Prog

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

Crossrefs

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

Sequence in context: A222308 A166812 A262844 * A086934 A009469 A222190

Adjacent sequences: A166938 A166939 A166940 * A166942 A166943 A166944

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Oct 24 2009

Extensions

Edited and offset corrected by Klaus Brockhaus, Nov 14 2009

Status

approved