A226292 (10*n^2+4*n+(1-(-1)^n))/8.

2, 6, 13, 22, 34, 48, 65, 84, 106, 130, 157, 186, 218, 252, 289, 328, 370, 414, 461, 510, 562, 616, 673, 732, 794, 858, 925, 994, 1066, 1140, 1217, 1296, 1378, 1462, 1549, 1638, 1730, 1824, 1921, 2020, 2122, 2226, 2333, 2442, 2554, 2668, 2785, 2904, 3026, 3150

Offset: 1

Author

Yosu Yurramendi, Jun 02 2013

Keywords

• nonn
• easy

Comments

The number of binary pattern classes in the (3,n)-rectangular grid with 2 '1's and (n-2) '0's: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other, n<10.

Column k=2 of A226290.

For n even, a(n) is A202803; for n odd, a(n) is A190816.

Number of lattice points (x,y) in the region bounded by y < 3x, y > x/2 and x <= n. - Wesley Ivan Hurt, Oct 31 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A190816, A202803, A226290.

Programs

Magma

[(10*n^2+4*n+(1-(-1)^n))/8: n in [1..50]]; // Vincenzo Librandi, Sep 04 2013

Maple

A226292:=n->(10*n^2+4*n+(1-(-1)^n))/8: seq(A226292(n), n=1..50); # Wesley Ivan Hurt, Oct 31 2014

Mathematica

CoefficientList[Series[(2 + 2 x + x^2) / ((1 + x) (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 04 2013 *)
LinearRecurrence[{2,0,-2,1},{2,6,13,22},60] (* Harvey P. Dale, Feb 01 2019 *)

Formula

a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>4, a(1)=2, a(2)=6, a(3)=13, a(4)=22.

a(n) = 2*a(n-2)-a(n-4)+10 for n>4, a(1)=2, a(2)=6, a(3)=13, a(4)=22.

a(n) = a(n-1)+a(n-2)-a(n-3)+5 for n>3, a(1)=2, a(2)=6, a(3)=13.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+(-1)^n for n>3, a(1)=2, a(2)=6, a(3)=13.

a(n) = 2*a(n-1)-a(n-2)+2+(1-(-1)^n)/2 for n>2, a(1)=2, a(2)=6.

G.f.: x*(2+2*x+x^2)/((1+x)*(1-x)^3). - Bruno Berselli, Jun 03 2013

Extensions

More terms from Vincenzo Librandi, Sep 04 2013