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A082395 Number of shifted Young tableaux with height <= 3. 4
1, 1, 2, 3, 6, 12, 27, 63, 154, 386, 989, 2574, 6787, 18085, 48622, 131719, 359194, 985186, 2715973, 7521568, 20915257, 58373587, 163462816, 459136810, 1293223231, 3651864607, 10336625732, 29321683083, 83344398534, 237344961292 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

Fouad Ibn-Majdoub-Hassani. Combinatoire de polyominos et des tableaux decales oscillants . These de Doctorat. Laboratoire de Recherche en Informatique, Universite Paris-Sud XI, France.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{k=1..n}(-1)^(k+1)*binomial(n, k)*binomial(k-1, floor(k/2)). - Vladeta Jovovic, Sep 18 2003

Recurrence: 3*(n-2)*a(n-3)+(2-n)*a(n-2)+(4-3*n)*a(n-1)+n*a(n)=0. - Vaclav Kotesovec, Oct 02 2012

Asymptotic: a(n) ~ 3^(n+3/2)/(16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 02 2012

MATHEMATICA

Table[Sum[(-1)^(k+1)*Binomial[n, k]*Binomial[k-1, Floor[k/2]], {k, 1, n}], {n, 1, 20}]

RecurrenceTable[{3*(n-2)*a[n-3]+(2-n)*a[n-2]+(4-3n)*a[n-1]+n*a[n]==0, a[1]==1, a[2]==1, a[3]==2}, a, {n, 20}] (* Vaclav Kotesovec, Oct 02 2012 *)

PROG

(Sage)

def A082395():

    a, b, s, n = 1, 0, 1, 1

    yield a

    while True:

        s += b

        yield s

        n += 1

        a, b = b, (2*b+3*a)*(n-1)/(n+1)

A082395_list = A082395()

[A082395_list.next() for i in range(30)] # Peter Luschny, Sep 24 2014

CROSSREFS

Partial sums of A005043.

Sequence in context: A186771 A019525 A108915 * A061343 A057649 A104872

Adjacent sequences:  A082392 A082393 A082394 * A082396 A082397 A082398

KEYWORD

nonn

AUTHOR

Fouad IBN MAJDOUB HASSANI, Apr 14 2003

EXTENSIONS

More terms from Vladeta Jovovic, Sep 18 2003

STATUS

approved

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Last modified April 25 23:17 EDT 2017. Contains 285426 sequences.