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Revision History for A058395
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Square array read by antidiagonals. Based on triangular numbers (A000217) with each term being the sum of 2 consecutive terms in the previous row.
(history; published version)
(history; published version)
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DATA
1, 0, 1, 3, 1, 1, 0, 3, 2, 1, 6, 3, 4, 3, 1, 0, 6, 6, 6, 4, 1, 10, 6, 9, 10, 9, 5, 1, 0, 10, 12, 15, 16, 13, 6, 1, 15, 10, 16, 21, 25, 25, 18, 7, 1, 0, 15, 20, 28, 36, 41, 38, 24, 8, 1, 21, 15, 25, 36, 49, 61, 66, 56, 31, 9, 1, 0, 21, 30, 45, 64, 85, 102, 104, 80, 39, 10, 1, 28, 21, 36, 55, 81, 113, 146, 168, 160, 111, 48, 11, 1
MATHEMATICA
T[0, k_] := If[OddQ[k], 0, (k+2)(k+4)/8];
T[n_, k_] := T[n, k] = If[k == 0, 1, T[n-1, k-1] + T[n-1, k]];
Table[T[n-k, k], {n, 0, 12}, {k, n, 0, -1}] // Flatten (* Jean-François Alcover, Apr 13 2023 *)
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reviewed
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CROSSREFS
Rows are A000217 with zeros, A008805, A002620, A000217, A000290, A001844, A005899 etc. Columns are A000012, A001477, A016028 etc. Diagonals include A058396, A049611, A001793, A001788, A055580, A055581, A055582 etc. The triangle A055252 also appears in half of the array.
Rows are A000217 with zeros, A008805, A002620, A000217, A000290, A001844, A005899.
Columns are A000012, A001477, A016028.
Diagonals include A058396, A049611, A001793, A001788, A055580, A055581, A055582.
The triangle A055252 also appears in half of the array.
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approved
editing
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approved
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EXAMPLE
[0] 1, 0, 3, 0, 6, 0, 10, 0, 15, 0, ...
[1] 1, 1, 3, 3, 6, 6, 10, 10, 15, 15, ...
[2] 1, 2, 4, 6, 9, 12, 16, 20, 25, 30, ...
[3] 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
[4] 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ...
[5] 1, 5, 13, 25, 41, 61, 85, 113, 145, 181, ...
[6] 1, 6, 18, 38, 66, 102, 146, 198, 258, 326, ...
[7] 1, 7, 24, 56, 104, 168, 248, 344, 456, 584, ...
[8] 1, 8, 31, 80, 160, 272, 416, 592, 800, 1040, ...