A016215 Expansion of 1 / ((1-x) * (1-3*x) * (1-10*x)).

1, 14, 153, 1570, 15821, 158574, 1586833, 15871610, 158725941, 1587288934, 15872977913, 158730044850, 1587301245661, 15873014848094, 158730155655393, 1587301578077290, 15873015845342981, 158730158647140054, 1587301587052531273, 15873015872268704930

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (14,-43,30).

Programs

Maple

a:= n-> add((10^(n+1-j)-3^(n+1-j))/7, j=0..n): seq(a(n), n=0..20); # Zerinvary Lajos, Jan 15 2007

Mathematica

CoefficientList[Series[1/((1-x)(1-3x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{14,-43,30},{1,14,153},30] (* Harvey P. Dale, Aug 17 2017 *)

Formula

a(0)=1, a(1)=14, a(n)=13*a(n-1)-30*a(n-2)+1. - Vincenzo Librandi, Feb 10 2011

a(n) = (1/18)-(9/14)*(3)^n+(100/63)*(10)^n. Antonio Alberto Olivares, May 12 2012