A019623 Expansion of 1/((1-4*x)*(1-7*x)*(1-11*x)).

1, 22, 335, 4400, 53661, 628122, 7178395, 80862100, 902846921, 10025125022, 110934086055, 1224883116600, 13505988249781, 148791855626722, 1638292574483315, 18032294531183900, 198432777621062241

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (22,-149,308).

Formula

a(n) = 4^(n+2)/21 + 11^(n+2)/28 - 7^(n+2)/12. - R. J. Mathar, Nov 11 2012

a(0)=1, a(1)=22, a(2)=335; for n>2, a(n)= 22*a(n-1) -149*a(n-2) +308*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 18*a(n-1) -77*a(n-2) +4^n. - Vincenzo Librandi, Jul 03 2013

E.g.f.: exp(4*x)*(64 - 343*exp(3*x) + 363*exp(7*x))/84. - Stefano Spezia, Feb 03 2021

Mathematica

CoefficientList[Series[1 / ((1 - 4 x) (1 - 7 x) (1 - 11 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{22, -149, 308}, {1, 22, 335}, 30] (* G. C. Greubel, Jan 28 2018 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-7*x)*(1-11*x)))); /* or */ I:=[1, 22, 335]; [n le 3 select I[n] else 22*Self(n-1)-149*Self(n-2)+308*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013
(PARI) x='x+O('x^30); Vec(1/((1-4*x)*(1-7*x)*(1-11*x))) \\ G. C. Greubel, Jan 28 2018

Crossrefs

Cf. A021884 (partial sums).

Sequence in context: A048795 A068186 A021284 * A021794 A348134 A223812

Adjacent sequences: A019620 A019621 A019622 * A019624 A019625 A019626

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved