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A109363
a(n) = 4*2^n - 3*n - 5.
3
-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
0,3
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)
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
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 *)
CROSSREFS
Cf. A000295.
Sequence in context: A273566 A217866 A256539 * A218214 A146213 A344311
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Aug 22 2005
STATUS
approved