cp's OEIS Frontend

The sequence is constructed from a truncated version of Pascal's Triangle.

1

1 1

1 2 1

3 3 1

3 6 4 1

9 10 5 1

9 19 15 6 1

28 34 21 7 1

28 62 55 28 8

90 117 83 36 8

90 207 200 119 44

297 407 319 163 44

...

After truncation the sequence appears as the left vertical column. The right column sequence can be found in A370568. a(n) arises from the Gambler's Ruin problem and it represents the number of ways a gambler is ruined in the Gambler's Ruin problem starting with $3 and with a maximum $11 causing retirement.