A017952 Expansion of 1/((1-3x)(1-6x)(1-10x)).

1, 19, 253, 2935, 31861, 333919, 3431773, 34875415, 352106821, 3541203919, 35532912493, 356054541895, 3564898452181, 35675104315519, 356907766700413, 3570018022624375, 35705822403011941, 357092077219868719, 3571123891724603533, 35712457635563794855

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (19,-108,180).

Formula

a(n) = (3*10^(n+2) - 7*6^(n+2) + 4*3^(n+2))/84. - Yahia Kahloune, May 19 2013

a(0)=1, a(1)=19, a(2)=253; for n>2, a(n) = 19*a(n-1) -108*a(n-2) +180*a(n-3). - Vincenzo Librandi, Jul 02 2013

a(n) = 16*a(n-1) -60*a(n-2) +3^n. - Vincenzo Librandi, Jul 02 2013

Maple

a:= n-> (Matrix(3, (i, j)-> `if`(i=j-1, 1, `if`(j=1, [19, -108, 180][i], 0)))^n)[1, 1]: seq(a(n), n=0..25);  # Alois P. Heinz, Jul 02 2013

Mathematica

CoefficientList[Series[1 / ((1 - 3 x) (1 - 6 x) (1 - 10 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{19, -108, 180}, {1, 19, 253}, 20] (* Harvey P. Dale, Jul 20 2024 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-6*x)*(1-10*x)))); /* or */ I:=[1, 19, 253]; [n le 3 select I[n] else 19*Self(n-1)-108*Self(n-2)+180*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013

Crossrefs

Sequence in context: A125454 A293917 A009762 * A055433 A185425 A009728

Adjacent sequences: A017949 A017950 A017951 * A017953 A017954 A017955

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved