A272134 a(n) = n*(15*n^2 - 15*n + 4).

0, 4, 68, 282, 736, 1520, 2724, 4438, 6752, 9756, 13540, 18194, 23808, 30472, 38276, 47310, 57664, 69428, 82692, 97546, 114080, 132384, 152548, 174662, 198816, 225100, 253604, 284418, 317632, 353336, 391620, 432574, 476288, 522852, 572356, 624890, 680544

Offset: 0

Author

Vincenzo Librandi, Apr 27 2016

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014. (page 16)
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A049450, A272357.

Programs

Magma

[n*(15*n^2-15*n+4): n in [0..40]];

Mathematica

Table[n (15 n^2 - 15 n + 4), {n, 0, 40}]

PARI

vector(100, n, n--; n*(15*n^2 - 15*n + 4)) \\ Altug Alkan, Apr 28 2016

Python

for n in range(0,10**3):print(n*(15*n**2-15*n+4),end=", ") # Soumil Mandal, Apr 30 2016

Formula

O.g.f.: 2*x*(2 + 26*x + 17*x^2)/(1-x)^4.

E.g.f.: x*(4 + 30*x + 15*x^2)*exp(x).

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

See page 7 in Brent's paper:

a(n) = 2*n^2*A049450(n) - n*(2*n-1)*A049450(n-1).

A272357(n) = 2*n^2*a(n) - n*(2*n-1)*a(n-1).