A137247 - OEIS

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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

Essentially the partial sums of A052103. - R. J. Mathar, Apr 01 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,6,-3).

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