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

0,2

Links

Table of n, a(n) for n=0..26.

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

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

Example

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

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 *)

Crossrefs

Sequence in context: A048478 A001360 A294838 * A261478 A199207 A088131

Adjacent sequences: A116949 A116950 A116951 * A116953 A116954 A116955

Keyword

nonn,easy

Author

Parthasarathy Nambi, Mar 29 2006

Extensions

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

More terms from Colin Barker, Jul 18 2013

Status

approved