A213826 Principal diagonal of the convolution array A213825.

2, 34, 132, 332, 670, 1182, 1904, 2872, 4122, 5690, 7612, 9924, 12662, 15862, 19560, 23792, 28594, 34002, 40052, 46780, 54222, 62414, 71392, 81192, 91850, 103402, 115884, 129332, 143782, 159270, 175832, 193504, 212322, 232322, 253540, 276012, 299774

Offset: 1

Author

Clark Kimberling, Jul 04 2012

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A213825.

Programs

Magma

[6*n^3-3*n^2-n: n in [1..40]]; // Vincenzo Librandi, Nov 23 2018

Mathematica

(See A213825.)
CoefficientList[Series[2 (1 + 13 x + 4 x^2) / (1 - x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Nov 23 2018 *)

Formula

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

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

G.f.: f(x)/g(x), where f(x) = 2*x*(1 + 13*x + 4*x^2) and g(x) = (1-x)^4.

a(n) = 2*A024215(n).

E.g.f.: (2 + 32*x + 33*x^2 + 6*x^3)*exp(x). - Franck Maminirina Ramaharo, Nov 23 2018