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A121956 a(n) = a(n-1) + (n-2)*a(n-2) + a(n-3) starting a(0)=0, a(1)=a(2)=1. 1
0, 1, 1, 2, 5, 12, 34, 99, 315, 1042, 3661, 13354, 51006, 201561, 826987, 3498286, 15277665, 68578942, 316519868, 1497639547, 7263576113, 36035247374, 182804409181, 946808180148, 5004540429504, 26963932982089, 148019711470333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..795

MAPLE

with(combinat);

a:= proc(n) option remember;

      if n<3 then fibonacci(n)

    else a(n-1) + (n-2)*a(n-2) + a(n-3)

      fi;

    end:

seq(a(n), n=0..30); # G. C. Greubel, Oct 06 2019

MATHEMATICA

M = {{0, 1, 0}, {0, 0, 1}, {1, n, 1}}; v[0]= {0, 1, 1}; v[n_]:= v[n]= M.v[n-1]; Table[v[n][[1]], {n, 0, 30}]

a[n_]:= a[n]= If[n<3, Fibonacci[n], a[n-1] + (n-2)*a[n-2] + a[n-3]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 06 2019 *)

PROG

(PARI) my(m=30, v=concat([0, 1, 1], vector(m-3))); for(n=4, m, v[n]=v[n-1]+(n-3)*v[n-2]+v[n-3]); v \\ G. C. Greubel, Oct 06 2019

(MAGMA) I:=[0, 1, 1]; [n le 3 select I[n] else Self(n-1) + (n-3)*Self(n-2) + Self(n-3): n in [1..30]]; // G. C. Greubel, Oct 06 2019

(Sage)

@CachedFunction

def a(n):

    if (n<3): return fibonacci(n)

    else: return a(n-1) + (n-2)*a(n-2) + a(n-3)

[a(n) for n in (0..30)] # G. C. Greubel, Oct 06 2019

(GAP)

a:= function(n)

    if n<3 then return Fibonacci(n);

    else return a(n-1) + (n-2)*a(n-2) + a(n-3);

    fi;

  end;

List([0..30], n-> a(n) ); # G. C. Greubel, Oct 06 2019

CROSSREFS

Sequence in context: A196545 A032292 A151408 * A176638 A131467 A000103

Adjacent sequences:  A121953 A121954 A121955 * A121957 A121958 A121959

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Sep 01 2006

EXTENSIONS

Definition replaced by recurrence - the Assoc. Eds. of the OEIS, Mar 27 2010

Offset changed by G. C. Greubel, Oct 06 2019

STATUS

approved

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Last modified June 15 21:26 EDT 2021. Contains 345051 sequences. (Running on oeis4.)