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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).

%I A373169 #33 Jun 08 2024 08:53:43
%S A373169 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,
%T A373169 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,
%U A373169 18,46,29,81,91,29,81,46,2,1,12,3,43,75,6,112,12,54,1,57,3
%N 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).
%C A373169 Row n is the zeroless analog of the positive n-gonal numbers.
%H A373169 Paolo Xausa, <a href="/A373169/b373169.txt">Table of n, a(n) for n = 2..11326</a> (first 150 antidiagonals, flattened).
%H A373169 Wikipedia, <a href="https://en.wikipedia.org/wiki/Polygonal_number">Polygonal number</a>.
%e A373169 The array begins:
%e A373169   n\k|  1  2   3   4   5    6    7    8    9   10  ...
%e A373169   ----------------------------------------------------
%e A373169    2 |  1, 2,  3,  4,  5,   6,   7,   8,   9,   1, ... = A177274
%e A373169    3 |  1, 3,  6,  1,  6,  12,  19,  27,  36,  46, ... = A243658 (from n = 1)
%e A373169    4 |  1, 4,  9, 16, 25,  36,  49,  64,  81,   1, ... = A370812
%e A373169    5 |  1, 5, 12, 22, 35,  51,   7,  29,  54,  82, ... = A373171
%e A373169    6 |  1, 6, 15, 28, 45,  66,  91,  12,  45,  82, ... = A373172
%e A373169    7 |  1, 7, 18, 34, 55,  81, 112, 148, 189, 235, ...
%e A373169    8 |  1, 8, 21,  4, 29,   6,  43,  86, 135,  19, ...
%e A373169    9 |  1, 9, 24, 46, 75, 111, 154,  24,  81, 145, ...
%e A373169   10 |  1, 1, 18, 43, 76, 117, 166, 223, 288, 361, ...
%e A373169   ...      |                                     \______ A373170 (main diagonal)
%e A373169         A004719 (from n = 2)
%t A373169 noz[n_] := FromDigits[DeleteCases[IntegerDigits[n], 0]];
%t A373169 A373169[n_, k_] := A373169[n, k] = If[k == 1, 1, noz[A373169[n, k-1] + (k-1)*(n-2) + 1]];
%t A373169 Table[A373169[n - k + 1, k], {n, 2, 15}, {k, n - 1}]
%o A373169 (PARI) noz(n) = fromdigits(select(sign, digits(n)));
%o A373169 T(n,k) = if (k==1, 1, noz(T(n,k-1) + (k-1)*(n-2) + 1));
%o A373169 matrix(7,7,n,k,T(n+1,k)) \\ _Michel Marcus_, May 30 2024
%Y A373169 Cf. rows 2..6: A177274, A243658, A370812, A373171, A373172.
%Y A373169 Cf. A373170 (main diagonal).
%Y A373169 Cf. A004719, A057145.
%K A373169 nonn,tabl,base,easy
%O A373169 2,3
%A A373169 _Paolo Xausa_, May 27 2024