A268484 a(n) = (n + 1)*(4*n^2 + 14*n + 9)/3.

3, 18, 53, 116, 215, 358, 553, 808, 1131, 1530, 2013, 2588, 3263, 4046, 4945, 5968, 7123, 8418, 9861, 11460, 13223, 15158, 17273, 19576, 22075, 24778, 27693, 30828, 34191, 37790, 41633, 45728, 50083, 54706, 59605, 64788, 70263, 76038, 82121, 88520, 95243

Offset: 0

Author

Ilya Gutkovskiy, Feb 12 2016

Keywords

• nonn
• easy

Examples

			a(0) = 1*3 = 3;
a(1) = 1*3 + 3*5 = 18;
a(2) = 1*3 + 3*5 + 5*7 = 53;
a(3) = 1*3 + 3*5 + 5*7 + 7*9 = 116, etc.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000466, A005408, A007290, A135036.

Programs

Mathematica

Table[(n + 1) ((4 n^2 + 14 n + 9)/3), {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {3, 18, 53, 116}, 40]

PARI

a(n)=(n+1)*(4*n^2+14*n+9)/3 \\ Charles R Greathouse IV, Jul 26 2016

Formula

G.f.: (3 + 6*x - x^2)/(x - 1)^4.

a(n) = Sum_{k = 0..n} (2*k + 1)*(2*k + 3) = Sum_{k = 0..n} A005408(k)*A005408(k + 1).

Sum_{n>=0} 1/a(n) = 0.4315109123788144393864...