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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
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 * A316219 A034740 A367293
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Jean-François Alcover, Dec 03 2015
STATUS
approved

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Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)