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

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

Adjacent sequences: A137244 A137245 A137246 * A137248 A137249 A137250

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