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A139756 Binomial transform of A004526. 3
0, 0, 1, 4, 12, 32, 80, 192, 448, 1024, 2304, 5120, 11264, 24576, 53248, 114688, 245760, 524288, 1114112, 2359296, 4980736, 10485760, 22020096, 46137344, 96468992, 201326592, 419430400, 872415232, 1811939328, 3758096384 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Essentially the same as A001787, A097067, A085750 and A118442.

Also: self-convolution of A131577. - R. J. Mathar, May 22 2008

Let S be a subset of {1,2,...,n}.  A succession in S is a subset of the form {i,i+1}.  a(n) is the total number of successions in all subsets of {1,2,...,n}.  a(n) = Sum_{k=1,2,...} A076791(n,k)*k. - Geoffrey Critzer, Mar 18 2012.

REFERENCES

I Goulden and D Jackson, Combinatorial Enumeration, John Wiley and Sons, 1983, page 55.

LINKS

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

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

FORMULA

O.g.f.: x^2/(1-2*x)^2. a(n) = (n-1)*2^n/4 if n>0. - R. J. Mathar, May 22 2008

a(n) = A097067(n), n>0. [From R. J. Mathar, Nov 03 2008]

a(n) = A168511(n+1,n). - Philippe Deléham, Mar 20 2013

a(n) = 2*a(n-1) + 2^(n-2), n>=2. - Philippe Deléham, Mar 20 2013

EXAMPLE

a(4) = 12 because we have {1,2}, {2,3}, {3,4}, {1,2,4}, {1,3,4} with one succession; {1,2,3}, {2,3,4} with two successions; and {1,2,3,4} with three successions. - Geoffrey Critzer, Mar 18 2012.

MATHEMATICA

nn = 30; a = 1/(1 - y x); b = x/(1 - y x) + 1; c = 1/(1 - x); CoefficientList[ D[Series[c b/(1 - (a x^2 c)), {x, 0, nn}], y] /. y -> 1, x]  (*Geoffrey Critzer, Mar 18 2012*)

CROSSREFS

Sequence in context: A090634 A260186 A097067 * A085750 A001787 A118442

Adjacent sequences:  A139753 A139754 A139755 * A139757 A139758 A139759

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, May 19 2008

EXTENSIONS

More terms from R. J. Mathar, May 22 2008

STATUS

approved

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Last modified February 16 21:59 EST 2019. Contains 320200 sequences. (Running on oeis4.)