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A289207 a(n) = max(0, n-2).

%I A289207 #21 Jul 01 2023 16:06:15
%S A289207 0,0,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
%T A289207 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
%U A289207 48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69
%N A289207 a(n) = max(0, n-2).
%C A289207 This simple sequence is such that there is one and only one array of differences D(n,k) where the first and the second upper subdiagonal is a(n).
%C A289207 The rows of this array are existing sequences of the OEIS, prepended with zeros:
%C A289207 row 0 is A118425,
%C A289207 row 1 is A006478,
%C A289207 row 2 is A001629,
%C A289207 row 3 is A010049,
%C A289207 row 4 is A006367,
%C A289207 row 5 is not in the OEIS.
%C A289207 It can be observed that a(n) is an autosequence of the first kind whose second kind mate is A199969. In addition, the structure of the array D(n,k) shows that the first row is an autosequence.
%C A289207 For n = 1 to 8, rows with only one leading zero are also autosequences.
%H A289207 OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%H A289207 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1).
%F A289207 G.f.: x^3 / (1-x)^2.
%e A289207 Array of differences begin:
%e A289207    0,   0,   0,   0,  0,   0,  0,  1,  4, 12, 30, 68, ...
%e A289207    0,   0,   0,   0,  0,   0,  1,  3,  8, 18, 38, 76, ...
%e A289207    0,   0,   0,   0,  0,   1,  2,  5, 10, 20, 38, 71, ...
%e A289207    0,   0,   0,   0,  1,   1,  3,  5, 10, 18, 33, 59, ...
%e A289207    0,   0,   0,   1,  0,   2,  2,  5,  8, 15, 26, 46, ...
%e A289207    0,   0,   1,  -1,  2,   0,  3,  3,  7, 11, 20, 34, ...
%e A289207    0,   1,  -2,   3, -2,   3,  0,  4,  4,  9, 14, 24, ...
%e A289207    1,  -3,   5,  -5,  5,  -3,  4,  0,  5,  5, 10, 16, ...
%e A289207   -4,   8, -10,  10, -8,   7, -4,  5,  0,  6,  6, 17, ...
%e A289207   12, -18,  20, -18, 15, -11,  9, -5,  6,  0,  7,  7, ...
%e A289207   ...
%t A289207 a[n_] := Max[0, n - 2];
%t A289207 D[n_, k_] /; k == n + 1 := a[n]; D[n_, k_] /; k == n + 2 := a[n]; D[n_, k_] /; k > n + 2 := D[n, k] = Sum[D[n + 1, j], {j, 0, k - 1}]; D[n_, k_] /; k <= n := D[n, k] = D[n - 1, k + 1] - D[n - 1, k];
%t A289207 Table[D[n, k], {n, 0, 11}, {k, 0, 11}]
%Y A289207 Essentially the same as A023444. Cf. A001477, A118425, A006478, A001629, A010049, A006367, A199969.
%K A289207 nonn,less
%O A289207 0,5
%A A289207 _Jean-François Alcover_ and _Paul Curtz_, Jun 28 2017