A062106 - OEIS

A062106

Number of ways a black pawn (from any starting square on the second back rank) can (theoretically) end on the n-th square of the leftmost file counted from the back rank.

0, 1, 2, 6, 15, 40, 109, 302, 846, 2390, 6796, 19426, 55767, 160668, 464305, 1345282, 3906701, 11367696, 33135987, 96740610, 282831981, 827939880, 2426431239, 7118546874, 20904025380, 61439768166, 180725813478, 532004277518, 1567150286281, 4619399683540

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..30.

MAPLE

ChessPawnTriangle := proc(r, c) option remember;

if r < 2 or c < 1 then 0

elif 2 = r then 1

elif 4 = r then 1+add(ChessPawnTriangle(r-1, c+j), j=-1..1)

else add(ChessPawnTriangle(r-1, c+j), j=-1..1)

end: