Lozanić's triangle

Lozanić's triangle (sometimes called Losanitsch's triangle) is a triangular array of binomial coefficients in a manner very similar to that of Pascal's triangle. It is named after the Serbian chemist Sima Lozanić, who researched it in his investigation into the symmetries exhibited by rows of paraffins (archaic term for alkanes).

The first few lines of Lozanić's triangle are

listed in (sequence in the OEIS).

Like Pascal's triangle, outer edge diagonals of Lozanić's triangle are all 1s, and most of the enclosed numbers are the sum of the two numbers above. But for numbers at odd positions k in even-numbered rows n (starting the numbering for both with 0), after adding the two numbers above, subtract the number at position (k − 1)/2 in row n/2 − 1 of Pascal's triangle.

The diagonals next to the edge diagonals contain the positive integers in order, but with each integer stated twice  .

Moving inwards, the next pair of diagonals contain the "quarter-squares" ( ), or the square numbers and pronic numbers interleaved.

The next pair of diagonals contain the alkane numbers l(6, n) ( ). And the next pair of diagonals contain the alkane numbers l(7, n) ( ), while the next pair has the alkane numbers l(8, n) ( ), then alkane numbers l(9, n) ( ), then l(10, n) ( ), l(11, n) ( ), l(12, n) ( ), etc.

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