A166943 One third of product plus sum of six consecutive nonnegative numbers.

5, 247, 1689, 6731, 20173, 50415, 110897, 221779, 411861, 720743, 1201225, 1921947, 2970269, 4455391, 6511713, 9302435, 13023397, 17907159, 24227321, 32303083, 42504045, 55255247, 71042449, 90417651, 114004853, 142506055

Offset

0,1

Comments

a(n) = ((n*...*(n+5))+(n+...+(n+5)))/3, n >= 0.

Binomial transform of 5, 242, 1200, 2400, 2400, 1200, 240, 0, 0, 0, 0, ....

Links

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

Formula

a(n) = (n^6 + 15n^5 + 85n^4 + 225n^3 + 274n^2 + 126n + 15)/3. - Charles R Greathouse IV, Nov 04 2009

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6)+240 for n > 5; a(0)=5, a(1)=247, a(2)=1689, a(3)=6731, a(4)=20173, a(5)=50415. - Klaus Brockhaus, Nov 14 2009

G.f.: (5+212*x+65*x^2-80*x^3+55*x^4-20*x^5+3*x^6)/(1-x)^7. - Klaus Brockhaus, Nov 14 2009

Example

a(0) = (0*1*2*3*4*5+0+1+2+3+4+5)/3 = (0+15)/3 = 5.
a(1) = (1*2*3*4*5*6+1+2+3+4+5+6)/3 = (720+21)/3 = 247.

Mathematica

lst={}; Do[p=(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*n+(n+5)+(n+4)+(n+3)+(n+2)+(n+1)+n; AppendTo[lst, p/3], {n, 0, 5!}]; lst
(Plus@@#+Times@@#)/3&/@Partition[Range[0, 30], 6, 1] (* Harvey P. Dale, Nov 10 2009 *)

Prog

(Magma) [ (&*s + &+s)/3 where s is [n..n+5]: n in [0..25] ]; // Klaus Brockhaus, Nov 14 2009

Crossrefs

Cf. A001477 (nonnegative integers), A028387 (n+(n+1)^2), A167875, A166941, A166942.

Sequence in context: A361538 A215910 A097323 * A125533 A068727 A135095

Adjacent sequences: A166940 A166941 A166942 * A166944 A166945 A166946

Keyword

nonn,easy

Author

Vladimir Joseph Stephan Orlovsky, Oct 24 2009

Extensions

Edited and offset corrected by Klaus Brockhaus, Nov 14 2009

Status

approved