A005945 Number of n-step mappings with 4 inputs. (Formerly M4966)

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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

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

Adjacent sequences: A005942 A005943 A005944 * A005946 A005947 A005948

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by Michael Somos, Oct 29 2002

Status

approved