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A137247
a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 3*a(n-4), with initial terms 0, 0, 0, 1.
1
0, 0, 0, 1, 4, 10, 22, 49, 112, 256, 580, 1309, 2956, 6682, 15106, 34141, 77152, 174352, 394024, 890473, 2012404, 4547866, 10277806, 23227033, 52491280, 118626160, 268085740, 605852581, 1369179004, 3094236490, 6992730202, 15803018149
OFFSET
0,5
COMMENTS
Essentially the partial sums of A052103. - R. J. Mathar, Apr 01 2008
FORMULA
From R. J. Mathar, Apr 01 2008: (Start)
O.g.f.: x^3/((1-x)*(1-3*x+3*x^2-3*x^3)).
A052103(n) = a(n+2) - a(n+1). (End)
MAPLE
a[0]:=0: a[1]:=0: a[2]:=0: a[3]:=1: for n from 4 to 30 do a[n]:=4*a[n-1]-6*a[n-2]+6*a[n-3]-3*a[n-4] end do: seq(a[n], n=0..30); # Emeric Deutsch, Mar 17 2008
MATHEMATICA
LinearRecurrence[{4, -6, 6, -3}, {0, 0, 0, 1}, 41] (* G. C. Greubel, Apr 15 2021 *)
PROG
(Magma) I:=[0, 0, 0, 1]; [n le 4 select I[n] else 4*Self(n-1) -6*Self(n-2) +6*Self(n-3) -3*Self(n-4): n in [1..41]]; // G. C. Greubel, Apr 15 2021
(Sage)
def A137247_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^3/((1-x)*(1-3*x+3*x^2-3*x^3)) ).list()
A137247_list(40) # G. C. Greubel, Apr 15 2021
CROSSREFS
Cf. A052103.
Sequence in context: A118430 A178452 A324536 * A155407 A318416 A124697
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Mar 10 2008
EXTENSIONS
More terms from R. J. Mathar, Rolf Pleisch and Emeric Deutsch, Apr 01 2008
Name edited by Michel Marcus, Jan 29 2019
STATUS
approved