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A109363 a(n) = 4*2^n - 3*n - 5. 1
-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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..33.

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

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

MAPLE

a:=n->sum (2^j-3, j=3..n): seq(a(n), n=1..34); # Zerinvary Lajos, Jun 27 2007

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 *)

PROG

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)

CROSSREFS

Cf. A000295.

Sequence in context: A273566 A217866 A256539 * A218214 A146213 A176145

Adjacent sequences:  A109360 A109361 A109362 * A109364 A109365 A109366

KEYWORD

easy,sign

AUTHOR

Creighton Dement, Aug 22 2005

STATUS

approved

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Last modified August 22 11:15 EDT 2017. Contains 290946 sequences.