cp's OEIS Frontend

A166941 Product plus sum of four consecutive nonnegative numbers.

%I A166941 #14 Sep 08 2022 08:45:48
%S A166941 6,34,134,378,862,1706,3054,5074,7958,11922,17206,24074,32814,43738,
%T A166941 57182,73506,93094,116354,143718,175642,212606,255114,303694,358898,
%U A166941 421302,491506,570134,657834,755278,863162,982206,1113154,1256774
%N A166941 Product plus sum of four consecutive nonnegative numbers.
%C A166941 a(n) = (n*...*(n+3))+(n+...+(n+3)), n >= 0.
%C A166941 All terms are even.
%C A166941 Binomial transform of 2*A167858.
%H A166941 Vincenzo Librandi, <a href="/A166941/b166941.txt">Table of n, a(n) for n = 0..1000</a>
%F A166941 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]
%F A166941 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
%F A166941 G.f.: 2*(3 + 2*x + 12*x^2 - 6*x^3 + x^4)/(1-x)^5. - _Klaus Brockhaus_, Nov 14 2009
%e A166941 a(0) = 0*1*2*3+0+1+2+3 = 0+6 = 6.
%e A166941 a(1) = 1*2*3*4+1+2+3+4 = 24+10 = 34.
%t A166941 lst={};Do[p=(n+3)*(n+2)*(n+1)*n+(n+3)+(n+2)+(n+1)+n;AppendTo[lst,p],{n,0,5!}];lst
%o A166941 (Magma) [ &*s + &+s where s is [n..n+3]: n in [0..32] ]; // _Klaus Brockhaus_, Nov 14 2009
%Y A166941 Cf. A001477 (nonnegative integers), A167858 (3,14,36,36,12,0,0,0,...), A028387 (n+(n+1)^2), A167875, A166942, A166943.
%K A166941 nonn,easy
%O A166941 0,1
%A A166941 _Vladimir Joseph Stephan Orlovsky_, Oct 24 2009
%E A166941 Edited and offset corrected by _Klaus Brockhaus_, Nov 14 2009