A006961 Number of mappings from n points to themselves with in-degree <= 2.

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

Offset: 0

Author

Simon Plouffe

Keywords

• nonn
• easy
• nice

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).

Crossrefs

Cf. A001190.

Programs

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 *)

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

Extensions

More terms from Jean-François Alcover, Dec 03 2015