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A109363 a(n) = 4*2^n - 3*n - 5. 1

%I

%S -1,0,5,18,47,108,233,486,995,2016,4061,8154,16343,32724,65489,131022,

%T 262091,524232,1048517,2097090,4194239,8388540,16777145,33554358,

%U 67108787,134217648,268435373,536870826,1073741735,2147483556,4294967201,8589934494,17179869083,34359738264

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

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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4, -5, 2).

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

%F a(0)=-1, a(n) = 2*a(n-1) + 3*n - 1. - _Vincenzo Librandi_, Jan 29 2011

%F 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

%p a:=n->sum (2^j-3,j=3..n): seq(a(n),n=1..34); # _Zerinvary Lajos_, Jun 27 2007

%t f[n_]:=4*2^n-3*n-5; f[Range[0,20]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 28 2011 *)

%t LinearRecurrence[{4,-5,2},{-1,0,5},20] (* _Harvey P. Dale_, Jun 13 2011 *)

%o 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)

%Y Cf. A000295.

%K easy,sign

%O 0,3

%A _Creighton Dement_, Aug 22 2005

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Last modified December 14 21:33 EST 2017. Contains 296020 sequences.