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A166943 One third of product plus sum of six consecutive nonnegative numbers. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A144999 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

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Last modified July 5 20:21 EDT 2020. Contains 335473 sequences. (Running on oeis4.)