OFFSET
0,4
COMMENTS
Represents the mean of the first and third binomial transforms of C(n,2) Binomial transform of A082149.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (18,-132,504,-1056,1152,-512).
FORMULA
a(n) = C(n, 2)*(2^(n-2) + 4^(n-2))/2.
G.f.: (x^2/(1-2*x)^3 + x^2/(1-4*x)^3)/2.
G.f.: x^2*(36*x^3 - 30*x^2 + 9*x-1)/((1 - 2*x)^3*(4*x - 1)^3).
E.g.f.: x^2*exp(3*x)*cosh(x)/2.
From Bruno Berselli, Feb 12 2018: (Start)
E.g.f.: x^2*(1 + exp(2*x))*exp(2*x)/4.
a(n) = 2^(n-4)*(2^(n-2) + 1)*(n - 1)*n. (End)
MAPLE
A082150:=[seq(binomial(n, 2)*(2^(n-2)+4^(n-2))/2, n=0..23)]; # Muniru A Asiru, Feb 12 2018
MATHEMATICA
CoefficientList[Series[(x^2/(1-2*x)^3 + x^2/(1-4*x)^3)/2, {x, 0, 50}], x] (* or *) Table[Binomial[n, 2]*(2^(n-2) + 4^(n-2))/2, {n, 0, 30}] (* G. C. Greubel, Feb 10 2018 *)
LinearRecurrence[{18, -132, 504, -1056, 1152, -512}, {0, 0, 1, 9, 60, 360}, 30] (* Harvey P. Dale, Jan 17 2022 *)
PROG
(PARI) for(n=0, 30, print1(binomial(n, 2)*(2^(n-2) + 4^(n-2))/2, ", ")) \\ G. C. Greubel, Feb 10 2018
(Magma) [Binomial(n, 2)*(2^(n-2) + 4^(n-2))/2: n in [0..30]]; // G. C. Greubel, Feb 10 2018
(GAP) List([0..23], n-> Binomial(n, 2)*(2^(n-2)+4^(n-2))/2); # Muniru A Asiru, Feb 12 2018
(Maxima) makelist(2^(n-4)*(2^(n-2)+1)*(n-1)*n, n, 0, 30); /* Bruno Berselli, Feb 13 2018 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Apr 07 2003
STATUS
approved