cp's OEIS Frontend

A214659 a(n) = n*(7*n^2 - 3*n - 1)/3.

%I A214659 #30 Mar 12 2024 09:53:52
%S A214659 0,1,14,53,132,265,466,749,1128,1617,2230,2981,3884,4953,6202,7645,
%T A214659 9296,11169,13278,15637,18260,21161,24354,27853,31672,35825,40326,
%U A214659 45189,50428,56057,62090,68541,75424,82753,90542,98805,107556,116809,126578,136877
%N A214659 a(n) = n*(7*n^2 - 3*n - 1)/3.
%C A214659 a(n) = the sum of the n X n matrices of A204008. For example, for n = 3, the sum of the 9 elements of the 3 X 3 submatrix of A204008 is 1 + 4 + 7 + 4 + 5 + 8 + 7 + 8 + 9 = 53. - _J. M. Bergot_, Jul 15 2013
%H A214659 G. C. Greubel, <a href="/A214659/b214659.txt">Table of n, a(n) for n = 0..1000</a>
%H A214659 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A214659 a(n) = Sum_{k=0..n} A214604(n, k) for n > 0 (row sums).
%F A214659 a(n) = A002378(n) + A051673(n).
%F A214659 From _Wesley Ivan Hurt_, Apr 11 2015: (Start)
%F A214659 a(n) = (7*n^3 - 3*n^2 - n)/3.
%F A214659 G.f.: x*(1+10*x+3*x^2)/(1-x)^4.
%F A214659 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%F A214659 E.g.f.: (x/3)*(3 + 18*x + 7*x^2)*exp(x). - _G. C. Greubel_, Mar 09 2024
%p A214659 A214659:=n->(7*n^3-3*n^2-n)/3: seq(A214659(n), n=0..50); # _Wesley Ivan Hurt_, Apr 11 2015
%t A214659 Table[(7 n^3 -3 n^2 -n)/3, {n,0,50}] (* _Wesley Ivan Hurt_, Apr 11 2015 *)
%t A214659 LinearRecurrence[{4,-6,4,-1}, {0,1,14,53}, 51] (* _G. C. Greubel_, Mar 09 2024 *)
%o A214659 (Haskell)
%o A214659 a214659 n = ((7 * n - 3) * n - 1) * n `div` 3
%o A214659 (Magma) [(7*n^3-3*n^2-n)/3 : n in [0..50]]; // _Wesley Ivan Hurt_, Apr 11 2015
%o A214659 (SageMath) [(7*n^3-3*n^2-n)/3 for n in range(51)] # _G. C. Greubel_, Mar 09 2024
%Y A214659 Cf. A002378, A051673, A204008, A214604, A214675.
%K A214659 nonn,easy
%O A214659 0,3
%A A214659 _Reinhard Zumkeller_, Jul 25 2012