OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (18,-120,374,-567,408,-112).
FORMULA
a(n) = A142458(n+2,n).
G.f.: x*(1+21*x-36*x^2-40*x^3) / ((1-7*x)*(4*x-1)^2*(1-x)^3). - R. J. Mathar, Sep 14 2013
MAPLE
A142976:=n->5/9 + n^2/2 + 7*n/6 - 4^(n+1) * (2*n/3 + 10/9) + 5*7^(n+1)/9: seq(A142976(n), n=1..25); # Wesley Ivan Hurt, Oct 17 2017
MATHEMATICA
(* First program *)
T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k - m+1)*T[n-1, k, m]];
A142976[n_]:= T[n+2, n, 3];
Table[A142976[n], {n, 30}] (* modified by G. C. Greubel, Mar 16 2022 *)
(* Additional programs *)
CoefficientList[Series[(1 +21*x -36*x^2 -40*x^3)/((1-7*x)*(1-4*x)^2*(1-x)^3), {x, 0, 25}], x] (* Wesley Ivan Hurt, Oct 17 2017 *)
LinearRecurrence[{18, -120, 374, -567, 408, -112}, {1, 39, 546, 5482, 47175, 373809}, 40] (* Vincenzo Librandi, Oct 18 2017 *)
PROG
(Magma) [5/9 + n^2/2 + 7*n/6 - 4^(n+1) * (2*n/3 + 10/9) + 5*7^(n+1)/9: n in [1..25]]; // Wesley Ivan Hurt, Oct 17 2017
(Sage) [(1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)) for n in (1..30)] # G. C. Greubel, Mar 16 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Oct 01 2008
STATUS
approved