A116952 a(n) = 3*a(n-1) + 5 with a(0) = 1.

1, 8, 29, 92, 281, 848, 2549, 7652, 22961, 68888, 206669, 620012, 1860041, 5580128, 16740389, 50221172, 150663521, 451990568, 1355971709, 4067915132, 12203745401, 36611236208, 109833708629, 329501125892, 988503377681, 2965510133048, 8896530399149

Offset: 0

Author

Parthasarathy Nambi, Mar 29 2006

Keywords

• nonn
• easy

Examples

			The second term is 8 since a(1) = 3*a(0) + 5 = 3*1 + 5 = 8.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Programs

Maple

a:=n->(7*3^n-5)/2: seq(a(n),n=0..27);
a[0]:=1: for n from 1 to 27 do a[n]:=3*a[n-1]+5 od: seq(a[n],n=0..27);

Mathematica

a[0] := 1; a[n_] := 3a[n - 1] + 5; Table[a[n], {n, 0, 30}]
NestList[3#+5&,1,30] (* or *) LinearRecurrence[{4,-3},{1,8},30] (* Harvey P. Dale, Jul 20 2018 *)

Formula

a(n) = (7/2)*3^n-(5/2). - Emeric Deutsch, Apr 01 2006

a(n) = 4*a(n-1)-3*a(n-2). G.f.: (4*x+1) / ((x-1)*(3*x-1)). - Colin Barker, Jul 18 2013

Extensions

More terms from Emeric Deutsch and Stefan Steinerberger, Apr 01 2006

More terms from Colin Barker, Jul 18 2013