A199109 a(n) = (7*3^n + 1)/2.

4, 11, 32, 95, 284, 851, 2552, 7655, 22964, 68891, 206672, 620015, 1860044, 5580131, 16740392, 50221175, 150663524, 451990571, 1355971712, 4067915135, 12203745404, 36611236211, 109833708632, 329501125895, 988503377684, 2965510133051, 8896530399152, 26689591197455

Offset: 0

Author

Vincenzo Librandi, Nov 03 2011

Keywords

• nonn
• easy

Comments

Also the number of (not necessarily maximal) cliques in the (n+2)-Mycielski graph. - Eric W. Weisstein, Nov 29 2017

Examples

			Ternary....................Decimal
11...............................4
102.............................11
1012............................32
10112...........................95
101112.........................284
1011112........................851
10111112......................2552
101111112.....................7655
1011111112...................22964, etc.
- _Philippe Deléham_, Feb 16 2014
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Clique.
• Eric Weisstein's World of Mathematics, Mycielski Graph.
• Index entries for linear recurrences with constant coefficients, signature (4,-3).

Crossrefs

Cf. A000244, A003462, A005032 (first differences), A199110, A237930.

Programs

Magma

[(7*3^n+1)/2 : n in [0..30]];

Mathematica

Table[(7 3^n + 1)/2, {n, 0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
(7 3^Range[0, 20] + 1)/2 (* Eric W. Weisstein, Nov 29 2017 *)
LinearRecurrence[{4, -3}, {11, 32}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(4 - 5 x)/(1 - 4 x + 3 x^2), {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

PARI

a(n)=7*3^n\2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3*a(n-1) - 1.

a(n) = 4*a(n-1) - 3*a(n-2).

G.f.: (4-5*x)/((1-x)*(1-3*x)). - Bruno Berselli, Nov 03 2011

a(n) = A000244(n+1) + A003462(n) + 1 = A237930(n) + 1. - Philippe Deléham, Feb 16 2014

From Elmo R. Oliveira, Apr 02 2025: (Start)

E.g.f.: exp(x)*(7*exp(2*x) + 1)/2.

a(n) = A199110(n)/2. (End)