A373169 Square array read by ascending antidiagonals: T(n,k) = noz(T(n,k-1) + (k-1)*(n-2) + 1), with T(n,1) = 1, n >= 2, k >= 1, where noz(n) = A004719(n).
1, 1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 9, 1, 5, 1, 6, 12, 16, 6, 6, 1, 7, 15, 22, 25, 12, 7, 1, 8, 18, 28, 35, 36, 19, 8, 1, 9, 21, 34, 45, 51, 49, 27, 9, 1, 1, 24, 4, 55, 66, 7, 64, 36, 1, 1, 11, 18, 46, 29, 81, 91, 29, 81, 46, 2, 1, 12, 3, 43, 75, 6, 112, 12, 54, 1, 57, 3
Offset: 2
Examples
The array begins:
n\k| 1 2 3 4 5 6 7 8 9 10 ...
----------------------------------------------------
2 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, ... = A177274
3 | 1, 3, 6, 1, 6, 12, 19, 27, 36, 46, ... = A243658 (from n = 1)
4 | 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, ... = A370812
5 | 1, 5, 12, 22, 35, 51, 7, 29, 54, 82, ... = A373171
6 | 1, 6, 15, 28, 45, 66, 91, 12, 45, 82, ... = A373172
7 | 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, ...
8 | 1, 8, 21, 4, 29, 6, 43, 86, 135, 19, ...
9 | 1, 9, 24, 46, 75, 111, 154, 24, 81, 145, ...
10 | 1, 1, 18, 43, 76, 117, 166, 223, 288, 361, ...
... | \______ A373170 (main diagonal)
A004719 (from n = 2)
Links
- Paolo Xausa, Table of n, a(n) for n = 2..11326 (first 150 antidiagonals, flattened).
- Wikipedia, Polygonal number.
Crossrefs
Programs
-
Mathematica
noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]]; A373169[n_, k_] := A373169[n, k] = If[k == 1, 1, noz[A373169[n, k-1] + (k-1)*(n-2) + 1]]; Table[A373169[n - k + 1, k], {n, 2, 15}, {k, n - 1}]
-
PARI
noz(n) = fromdigits(select(sign, digits(n))); T(n,k) = if (k==1, 1, noz(T(n,k-1) + (k-1)*(n-2) + 1)); matrix(7,7,n,k,T(n+1,k)) \\ Michel Marcus, May 30 2024
Comments