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

1,1

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).

Formula

a(n) = -n - 3*n^2 + 6*n^3. [corrected by Christian Krause, Jan 24 2026]

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

Mathematica

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

Prog

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

Crossrefs

Cf. A213825.

Sequence in context: A200166 A226407 A226336 * A259108 A064202 A206624

Adjacent sequences: A213823 A213824 A213825 * A213827 A213828 A213829

Keyword

nonn,easy

Author

Clark Kimberling, Jul 04 2012

Status

approved