Tiling

Tiling a 2xN board with 1x2 tiles
a[0] = 1

a[1] = 1

a[n] = a[n-1] + a[n-2]

Sloane: A000045

UVa: 900

Note: These are also the Fibonacci numbers

Tiling a 2xN board with 1x2 tiles and 2x2 tiles
a[0] = 1

a[1] = 1

a[n] = a[n-1] + 2*a[n-2]

Sloane: A001045

Note: These are also the Jacobsthal numbers

Tiling a 2xN board with 1x1 tiles and L-shaped tiles (of area = 3)
a[0] = 1

a[1] = 1

a[2] = 5

a[n] = a[n-1] + 4*a[n-2] + 2*a[n-3]

Sloane: A127864

UVa: 11310

Tiling a 3xN board with 1x1 tiles and 2x2 tiles
a[0] = 1

a[1] = 1

a[n] = a[n-1] + 2*a[n-2]

Sloane: A001045

Note: These are also the Jacobsthal numbers