A271636 - OEIS

%I #40 Sep 08 2022 08:46:16

%S 0,28,152,468,1072,2060,3528,5572,8288,11772,16120,21428,27792,35308,

%T 44072,54180,65728,78812,93528,109972,128240,148428,170632,194948,

%U 221472,250300,281528,315252,351568,390572,432360,477028,524672,575388,629272,686420

%N a(n) = 4*n*(4*n^2 + 3).

%C This is the case h=0 of the identity 4*n*(4*n^2 + 3*(2*h + 1)^2) = (2*n - 2*h - 1)^3 + (2*n + 2*h + 1)^3.

%C Subsequence of A004999 and, after 0, second bisection of A153976.

%H Vincenzo Librandi, <a href="/A271636/b271636.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F O.g.f.: 4*x*(7 + 10*x + 7*x^2)/(1 - x)^4.

%F E.g.f.: 4*x*(7 + 12*x + 4*x^2)*exp(x). - _Ilya Gutkovskiy_, Apr 11 2016

%F a(n) = -a(-n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

%F a(n) = 4*A229183(2*n). - _Bruno Berselli_, Apr 11 2016

%t Table[4 n (4 n^2 + 3), {n, 0, 50}]

%o (Magma) [4*n*(4*n^2+3): n in [0..50]];

%o (PARI) x='x+O('x^99); concat(0, Vec(x*(28+40*x+28*x^2)/(1-x)^4)) \\ _Altug Alkan_, Apr 11 2016

%o (Python) for n in range(0,1000):print(4*n*(4*n**2+3)) # _Soumil Mandal_, Apr 11 2016

%Y Cf. A004999, A153976, A229183.

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Apr 11 2016

%E Edit and extended by _Bruno Berselli_, Apr 12 2016