A082149 A transform of C(n,2).

0, 0, 1, 6, 30, 140, 615, 2562, 10220, 39384, 147645, 541310, 1948650, 6908772, 24180611, 83702010, 286978200, 975725744, 3293074233, 11041484022, 36804946550, 122037454140, 402723598431, 1323234680306, 4330586226180

Offset

0,4

Comments

Represents the mean of C(n,2) with its second binomial transform. Binomial transform of A080929 (preceded by two zeros).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-57,136,-171,108,-27).

Formula

a(n) = C(n, 2)*(3^(n-2) + 1)/2.

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

G.f.: x^2(14*x^3-15*x^2+6*x-1)/((1-x)^3*(3*x-1)^3).

E.g.f.: x^2*exp(2*x)*cosh(x)/2.

Mathematica

CoefficientList[Series[(x^2/(1-3*x)^3 + x^2/(1-x)^3)/2, {x, 0, 50}], x] (* or *) Table[Binomial[n, 2]*(1 + 3^(n-2))/2, {n, 0, 30}] (* G. C. Greubel, Feb 10 2018 *)
LinearRecurrence[{12, -57, 136, -171, 108, -27}, {0, 0, 1, 6, 30, 140}, 30] (* Harvey P. Dale, Aug 11 2021 *)

Prog

(PARI) for(n=0, 30, print1(binomial(n, 2)*(1 + 3^(n-2))/2, ", ")) \\ G. C. Greubel, Feb 10 2018
(Magma) [Binomial(n, 2)*(1 + 3^(n-2))/2: n in [0..30]]; // G. C. Greubel, Feb 10 2018

Crossrefs

Cf. A082150, A000217, A027472.

Sequence in context: A001334 A125316 A092439 * A002457 A137400 A220830

Adjacent sequences: A082146 A082147 A082148 * A082150 A082151 A082152

Keyword

easy,nonn

Author

Paul Barry, Apr 07 2003

Status

approved