A282389 Number of squares in triangle-shaped polyominoes obtained by adding three identical polyominoes to the previous one, starting with one L-tetromino.

4, 10, 25, 70, 238, 901, 3445, 13390, 52942, 210226, 838450, 3350725, 13393093, 53547790, 214151950, 856558645, 3426077749, 13703917774, 54815043790, 219258602290, 877031899954, 3508124454085, 14032487779525, 56129938535185, 224519713993489, 898078755310654

Offset

0,1

Comments

Each polyomino a(n) has a width of A282390(n+1) squares and a height of A000051(n) squares.

Links

Table of n, a(n) for n=0..25.

Daniel Poveda Parrilla, Illustration of initial terms

Formula

a(0) = 4; a(n) = a(n-1) + 3*(A282390(n)*A000051(n-1) - a(n-1)) for n > 0.

a(n) = A282390(n+(n mod 2))*A000051(n-(n mod 2)) for n > 0.

a(n) = (A282390(n+(n mod 2)) - A000051(n-1+(n mod 2)))*A000051(n-(n mod 2)) + A028401(n+2) for n > 0.

Prog

(Python)
m = [3, 1]
for i in range(25):
    w, h = m[0], len(m)
    print(sum(m)) # print(w) for widths of the polyominoes
    m2 = [w-x for x in reversed(m) if w>x]
    m = [w+x for x in m2] + [w for x in m if x==w] + m2
# Andrey Zabolotskiy, Feb 14 2017

Crossrefs

Cf. A000051, A028401, A282390.

Sequence in context: A347725 A097136 A049348 * A361611 A145775 A283958

Adjacent sequences: A282386 A282387 A282388 * A282390 A282391 A282392

Keyword

nonn

Author

Daniel Poveda Parrilla, Feb 14 2017

Status

approved