A271636 a(n) = 4*n*(4*n^2 + 3).

0, 28, 152, 468, 1072, 2060, 3528, 5572, 8288, 11772, 16120, 21428, 27792, 35308, 44072, 54180, 65728, 78812, 93528, 109972, 128240, 148428, 170632, 194948, 221472, 250300, 281528, 315252, 351568, 390572, 432360, 477028, 524672, 575388, 629272, 686420

Offset: 0

Author

Vincenzo Librandi, Apr 11 2016

Keywords

• nonn
• easy

Comments

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.

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A004999, A153976, A229183.

Programs

Magma

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

Mathematica

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

PARI

x='x+O('x^99); concat(0, Vec(x*(28+40*x+28*x^2)/(1-x)^4)) \\ Altug Alkan, Apr 11 2016

Python

for n in range(0,1000):print(4*n*(4*n**2+3)) # Soumil Mandal, Apr 11 2016

Formula

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

E.g.f.: 4*x*(7 + 12*x + 4*x^2)*exp(x). - Ilya Gutkovskiy, Apr 11 2016

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

a(n) = 4*A229183(2*n). - Bruno Berselli, Apr 11 2016

Extensions

Edit and extended by Bruno Berselli, Apr 12 2016