A017293 a(n) = 10*n + 2.

2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122, 132, 142, 152, 162, 172, 182, 192, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 302, 312, 322, 332, 342, 352, 362, 372, 382, 392, 402, 412, 422, 432, 442, 452, 462, 472, 482, 492, 502, 512, 522, 532

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

Comments

Number of 5 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (11;0) and (01;1). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1A008574; m=3: A016933; m=4: A022144; m=6: A017569. - Sergey Kitaev, Nov 13 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Tanya Khovanova, Recursive Sequences.
• Sergey Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Subsequence of A034709, together with A017281, A139222, A139245, A017329, A139249, A139264, A139279 and A139280.

Cf. A008574, A008592, A016861, A016873, A016933, A017569, A022144.

Programs

Magma

[10*n+2: n in [0..50]]; // Vincenzo Librandi, May 04 2011

Maple

A017293:=n->10*n+2; seq(A017293(n), n=0..100); # Wesley Ivan Hurt, May 03 2014

Mathematica

Range[2, 1000, 10] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
CoefficientList[Series[(2 + 8 x) / (1 - x)^2, {x, 0, 30}], x] (* Vincenzo Librandi, Jul 23 2016 *)
10 Range[0,60]+2 (* or *) LinearRecurrence[{2,-1},{2,12},60] (* Harvey P. Dale, Jul 04 2019 *)

Formula

a(n) = 2*A016861(n) = A008592(n) + 2. - Wesley Ivan Hurt, May 03 2014

G.f.: 2*(1 + 4*x)/(1-x)^2. - Vincenzo Librandi, Jul 23 2016

From Elmo R. Oliveira, Apr 04 2025: (Start)

E.g.f.: 2*exp(x)*(1 + 5*x).

a(n) = 2*a(n-1) - a(n-2) for n >= 2.

a(n) = A016873(2*n). (End)