OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: (1 - 2*x + 3*x^2 - x^3)/(1-x)^6. - Colin Barker, Apr 15 2013
From R. J. Mathar, Sep 29 2020: (Start)
a(n) = (n+1)*(n+2)*(60 +12*n +7*n^2 +n^3)/120. (End)
From G. C. Greubel, Aug 01 2022: (Start)
a(n) = Sum_{j=1..2} binomial(n+2*j, 3*j-1).
E.g.f.: (1/120)*(120 + 360*x + 300*x^2 + 120*x^3 + 20*x^4 + x^5)*exp(x). (End)
MATHEMATICA
CoefficientList[Series[(1-2*x+3*x^2-x^3)/(1-x)^6, {x, 0, 60}], x] (* Vincenzo Librandi, Oct 18 2013 *)
Sum[Binomial[2*j +Range[0, 60], 3*j-1], {j, 2}] (* G. C. Greubel, Aug 01 2022 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 4, 12, 31, 71, 147}, 40] (* Harvey P. Dale, Feb 27 2023 *)
PROG
(Magma) [(60 +12*n +7*n^2 +n^3)*Binomial(n+2, 2)/60: n in [0..60]]; // G. C. Greubel, Aug 01 2022
(SageMath) [(60 +12*n +7*n^2 +n^3)*binomial(n+2, 2)/60 for n in (0..60)] # G. C. Greubel, Aug 01 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved