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

Author

Paul Curtz, Mar 10 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A052103.

Programs

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

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 *)

Sage

def A137247_list(prec):
    P. = 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

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)

Extensions

More terms from R. J. Mathar, Rolf Pleisch and Emeric Deutsch, Apr 01 2008

Name edited by Michel Marcus, Jan 29 2019