A142976 a(n) = (1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)).

1, 39, 546, 5482, 47175, 373809, 2824048, 20729340, 149474205, 1065892555, 7547929806, 53215791774, 374165893891, 2626319535477, 18415017346620, 129036833755984, 903819045351033, 6329115592649775, 44313888005135290, 310239730485553170

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 01 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A142458, A144380, A144381, A144414.

Programs

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

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 *)

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

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