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A130102 E.g.f.: (e^x-x)^2. 4
1, 0, 2, 2, 8, 22, 52, 114, 240, 494, 1004, 2026, 4072, 8166, 16356, 32738, 65504, 131038, 262108, 524250, 1048536, 2097110, 4194260, 8388562, 16777168, 33554382, 67108812, 134217674, 268435400, 536870854, 1073741764, 2147483586 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of length n binary sequences in which no symbol occurs exactly once. (The Rosenthal formula takes 2^n for the total number of binary sequences and subtracts n for each sequence of length n with a single 0 or 1). - Geoffrey Critzer, Dec 03 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = 2^n - 2n for n <> 2 (cf. A005803). - Rainer Rosenthal, Feb 14 2010.

E.g.f.: e^(2x)-2xe^x+x^2; a(n)=sum{k=0..n, C(n,k)*A060576(k)*A060576(n-k)}.

G.f. 1 +2x^2 -2*x^3/((2*x-1)*(x-1)^2). - R. J. Mathar, Dec 04 2011

EXAMPLE

a(4)=8 because there are 8 sequences on {0,1} such that neither 0 nor 1 occurs exactly once: {0,0,0,0}, {0,0,1,1}, {0,1,0,1}, {0,1,1,0}, {1,0,0,1}, {1,0,1,0}, {1,1,0,0}, {1,1,1,1}. - Geoffrey Critzer, Dec 03 2011

MATHEMATICA

a=Exp[x]-x; Range[0, 20]! CoefficientList[Series[a^2, {x, 0, 20}], x] (* Geoffrey Critzer, Dec 03 2011 *)

CoefficientList[Series[1+2x^2-2*x^3/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 28 2012 *)

PROG

(MAGMA) I:=[1, 0, 2, 2, 8, 22]; [n le 6 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 28 2012

CROSSREFS

Sequence in context: A208235 A151377 A151407 * A151384 A113464 A054093

Adjacent sequences:  A130099 A130100 A130101 * A130103 A130104 A130105

KEYWORD

nonn,easy

AUTHOR

Paul Barry, May 07 2007

STATUS

approved

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Last modified March 30 18:24 EDT 2017. Contains 284302 sequences.