A109363 a(n) = 4*2^n - 3*n - 5.

-1, 0, 5, 18, 47, 108, 233, 486, 995, 2016, 4061, 8154, 16343, 32724, 65489, 131022, 262091, 524232, 1048517, 2097090, 4194239, 8388540, 16777145, 33554358, 67108787, 134217648, 268435373, 536870826, 1073741735, 2147483556, 4294967201, 8589934494, 17179869083, 34359738264

Offset: 0

Author

Creighton Dement, Aug 22 2005

Keywords

• easy
• sign

Comments

This sequence appears alongside the Eulerian numbers A000295 in the batch of sequences generated by the floretion given in the program code.

Floretion Algebra Multiplication Program, FAMP Code: 4ibaseisumseq[ - .5'i - .75'j - .5i' - .75j' + .25'ii' + .25'jj' - 1.25'kk' - .25'ik' + .5'jk' - .25'ki' + .5'kj' + .75e]; sumtype: Y[8] = (int)Y[6] - (int)Y[7] + Y[8] + sum (internal program code).

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

Crossrefs

Cf. A000295, A036563.

Programs

Maple

A109363 := proc(n)
    4*2^n-3*n-5 ;
end proc:
seq(A109363(n),n=0..10) ; # R. J. Mathar, Jun 18 2019

Mathematica

f[n_]:=4*2^n-3*n-5; f[Range[0,20]] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2011 *)
LinearRecurrence[{4,-5,2},{-1,0,5},20] (* Harvey P. Dale, Jun 13 2011 *)

Formula

G.f.: (1-4*x)/((2*x-1)*(x-1)^2).

a(0)=-1, a(n) = 2*a(n-1) + 3*n - 1. - Vincenzo Librandi, Jan 29 2011

a(0)=-1, a(1)=0, a(2)=5, a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3). - Harvey P. Dale, Jun 13 2011

a(n) - a(n-1) = A036563(n+1). - R. J. Mathar, Jun 18 2019

E.g.f.: exp(x)*(4*exp(x) - 3*x - 5). - Elmo R. Oliveira, Mar 07 2025