A062704 -id:A062704 - cp's OEIS frontend

A062705 Array described in A062704 read by diagonals in direction of creation.

1, 1, 2, 1, 3, 5, 1, 6, 10, 13, 1, 14, 25, 34, 40, 1, 41, 76, 107, 131, 145, 1, 146, 278, 399, 500, 575, 616, 1, 617, 1193, 1734, 2209, 2594, 2871, 3017, 1, 3018, 5890, 8630, 11117, 13250, 14943, 16135, 16752

Offset: 1

Floor van Lamoen, Jul 11 2001

Cf. A062704, A062706.

A062706 The array of A062704 read by diagonals in the 'up' direction.

Original entry on oeis.org

1, 1, 2, 5, 3, 1, 1, 6, 10, 13, 40, 34, 25, 14, 1, 1, 41, 76, 107, 131, 145, 616, 575, 500, 399, 278, 146, 1, 1, 617, 1193, 1734, 2209, 2594, 2871, 3017, 16752, 16135, 14943, 13250, 11117, 8630, 5890, 3018, 1

Offset: 1

Floor van Lamoen, Jul 11 2001

Cf. A062705, A062704.

A063179 Di-Boustrophedon transform of (1,0,0,0,...): Fill in an array by diagonals alternating in the 'up' and 'down' directions. The n-th diagonal starts with the n-th element of (1,0,0,0,...). When going in the 'up' direction the next element is the sum of the previous element of the diagonal and the previous two elements of the row the new element is in. When going in the 'down' direction the next element is the sum of the previous element of the diagonal and the previous two elements of the column the new element is in. The final element of the n-th diagonal is a(n).

Original entry on oeis.org

1, 1, 2, 4, 12, 42, 178, 870, 4830, 29976, 205572, 1543210, 12583242, 110725638, 1045664646, 10547679660, 113172039256, 1286925785286, 15459448549274, 195616259182162, 2600506074185090, 36235386548738016, 528084808585261568, 8033872923106040478

Offset: 1

Floor van Lamoen, Jul 09 2001

			Array begins:
   1  1  0  4  0 42 ...
   0  1  3  4 38 ...
   2  2  7 31 ...
   0 10 22 ...
  12 12 ...
   0 ...

Cf. A000667, A059216, A062704, A063180, A063181.

More terms from Sean A. Irvine, Apr 21 2023

A063415 Triangle of coefficients of di-Boustrophedon transform (see A063179) read by rows: Let the original sequence be (U0,U1,...) and the transformed sequence (V0,V2,...), then Vn is a linear combination of U0,...,Un. T(n,m) is the coefficient that goes with Um to get Vn.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 4, 5, 3, 1, 12, 14, 9, 4, 1, 42, 51, 32, 14, 5, 1, 178, 214, 137, 60, 20, 6, 1, 870, 1049, 668, 295, 100, 27, 7, 1, 4830, 5820, 3713, 1636, 555, 154, 35, 8, 1, 29976, 36125, 23036, 10160, 3446, 952, 224, 44, 9, 1, 205572, 247734, 157993, 69664

Offset: 0

Floor van Lamoen, Jul 19 2001

			The triangle begins:
......1
....1...1
..2...2...1
4...5...3...1

T(n, 0) is A063179. Row sums form A062704. T(n, n-2) is A000096. Cf. A059718.

cp's OEIS Frontend

A062705 Array described in A062704 read by diagonals in direction of creation.

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A062706 The array of A062704 read by diagonals in the 'up' direction.

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A063415 Triangle of coefficients of di-Boustrophedon transform (see A063179) read by rows: Let the original sequence be (U0,U1,...) and the transformed sequence (V0,V2,...), then Vn is a linear combination of U0,...,Un. T(n,m) is the coefficient that goes with Um to get Vn.

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Examples

Crossrefs