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A019316
Expansion of 1/((1-4x)(1-6x)(1-7x)).
2
1, 17, 195, 1885, 16571, 137277, 1092715, 8456045, 64100091, 478409437, 3528167435, 25777174605, 186937014811, 1347606967997, 9667804397355, 69083038251565, 492036007548731, 3494997671436957, 24769526131110475
OFFSET
0,2
FORMULA
a(n) = 8*4^n/3 -18*6^n +49*7^n/3. - R. J. Mathar, Jun 29 2013
a(0)=1, a(1)=17, a(2)=195; for n>2, a(n) = 17*a(n-1) -94*a(n-2) +168*a(n-3). - Vincenzo Librandi, Jul 02 2013
a(n) = 13*a(n-1) -42*a(n-2) +4^n. - Vincenzo Librandi, Jul 02 2013
MAPLE
A019316:=n->8*4^n/3 -18*6^n +49*7^n/3: seq(A019316(n), n=0..30); # Wesley Ivan Hurt, Jan 27 2017
MATHEMATICA
CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 02 2013 *)
LinearRecurrence[{17, -94, 168}, {1, 17, 195}, 30] (* Harvey P. Dale, Aug 20 2017 *)
PROG
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-7*x)))); /* or */ I:=[1, 17, 195]; [n le 3 select I[n] else 17*Self(n-1)-94*Self(n-2)+168*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 02 2013
(PARI) Vec(1/((1-4*x)*(1-6*x)*(1-7*x)) + O(x^30)) \\ Michel Marcus, Jan 28 2017
CROSSREFS
Sequence in context: A140537 A359698 A021434 * A262111 A238672 A018250
KEYWORD
nonn,easy
STATUS
approved