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A006961 Number of mappings from n points to themselves with in-degree <= 2.
(Formerly M2584)
4
1, 1, 3, 6, 15, 31, 75, 164, 388, 887, 2092, 4884, 11599, 27443, 65509, 156427, 375263, 901353, 2171313, 5237581, 12658815, 30633725, 74238228, 180106656, 437437445, 1063425655, 2587564434, 6301175326, 15356071604, 37448674536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..29.

N. G. de Bruijn, D. A. Klarner, Multisets of aperiodic cycles, SIAM J. Algebraic Discrete Methods, 3 (1982), no. 3, 359-368. MR0666861(84i:05008).

FORMULA

Let T(x) = x+x^2+x^3+2*x^4+3*x^5+6*x^6+11*x^7+ ... be the g.f. for A001190. Then the g.f. here is 1/(Prod_{k=1..oo} (1-T(x^k))). - N. J. A. Sloane, Mar 25 2014

MATHEMATICA

max = 30; (* w(n) is A001190(n) *) w[0]=0; w[1]=1; w[n_] := w[n] = If[ OddQ[n], Sum[w[k]*w[n-k], {k, 1, (n-1)/2}], Sum[w[k]*w[n-k], {k, 1, n/2 - 1}] + (1/2)*w[n/2]*(1 + w[n/2]) ]; T[x_] := Sum[w[n] x^n, {n, 0, max}]; s = 1/Product[1-T[x^k], {k, 1, max}] + O[x]^max; CoefficientList[s, x] (* Jean-François Alcover, Dec 03 2015 *)

CROSSREFS

Cf. A001190.

Sequence in context: A244710 A244711 A244712 * A034740 A232973 A289006

Adjacent sequences:  A006958 A006959 A006960 * A006962 A006963 A006964

KEYWORD

nonn,easy,nice

AUTHOR

Simon Plouffe

EXTENSIONS

More terms from Jean-François Alcover, Dec 03 2015

STATUS

approved

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Last modified September 24 04:14 EDT 2017. Contains 292402 sequences.