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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 07 2003
STATUS
approved