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A005945
Number of n-step mappings with 4 inputs.
(Formerly M4966)
10
0, 1, 15, 60, 154, 315, 561, 910, 1380, 1989, 2755, 3696, 4830, 6175, 7749, 9570, 11656, 14025, 16695, 19684, 23010, 26691, 30745, 35190, 40044, 45325, 51051, 57240, 63910, 71079, 78765, 86986, 95760, 105105, 115039, 125580, 136746
OFFSET
0,3
COMMENTS
a(n) is the coefficient of x^4/4! in n-th iteration of exp(x)-1.
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346.
T. Hogg and B. A. Huberman, Attractors on finite sets: the dissipative dynamics of computing structures, Phys. Review A 32 (1985), 2338-2346. (Annotated scanned copy)
B. A. Huberman, T. H. Hogg, & N. J. A. Sloane, Correspondence, 1985
Pierpaolo Natalini, Paolo E. Ricci, Integer Sequences Connected with Extensions of the Bell Polynomials, Journal of Integer Sequences, 2017, Vol. 20, #17.10.2.
FORMULA
G.f.: x*(1+11*x+6*x^2)/(1-x)^4. a(n)=n*(3*n-1)*(2*n-1)/2.
For n>0, a(n) = n*A000567(n) - A000217(n-1). - Bruno Berselli, Apr 25 2010; Feb 01 2011
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 18 2012
a(n) = -A094952(-n) for all n in Z. - Michael Somos, Jan 23 2014
EXAMPLE
G.f. = x + 15*x^2 + 60*x^3 + 154*x^4 + 315*x^5 + 561*x^6 + 910*x^7 + ...
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 15, 60}, 50] (* Vincenzo Librandi, Jun 18 2012 *)
a[ n_] := 3 n^3 - 5/2 n^2 + 1/2 n; (* Michael Somos, Jun 10 2015 *)
PROG
(PARI) {a(n) = 3*n^3 - 5/2*n^2 + 1/2*n}; /* Michael Somos, Jan 23 2014 */
(Magma) I:=[0, 1, 15, 60]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..45]]; // Vincenzo Librandi Jun 18 2012
CROSSREFS
Cf. for recursive method [Ar(m) is the m-th term of a sequence in the OEIS] a(n) = n*Ar(n) - A000217(n-1) or a(n) = (n+1)*Ar(n+1) - A000217(n) or similar: A081436, A005920, A006003 and the terms T(2, n) or T(3, n) in the sequence A125860. [Bruno Berselli, Apr 25 2010]
Cf. A094952.
Sequence in context: A223344 A206238 A064761 * A223337 A110755 A206231
KEYWORD
nonn,easy
EXTENSIONS
Edited by Michael Somos, Oct 29 2002
STATUS
approved