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

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, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset

0,5

Comments

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).

The rows of this array are existing sequences of the OEIS, prepended with zeros:

row 0 is A118425,

row 1 is A006478,

row 2 is A001629,

row 3 is A010049,

row 4 is A006367,

row 5 is not in the OEIS.

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.

For n = 1 to 8, rows with only one leading zero are also autosequences.

Links

Table of n, a(n) for n=0..71.

OEIS Wiki, Autosequence

Index entries for linear recurrences with constant coefficients, signature (2, -1).

Formula

G.f.: x^3 / (1-x)^2.

Example

Array of differences begin:
   0,   0,   0,   0,  0,   0,  0,  1,  4, 12, 30, 68, ...
   0,   0,   0,   0,  0,   0,  1,  3,  8, 18, 38, 76, ...
   0,   0,   0,   0,  0,   1,  2,  5, 10, 20, 38, 71, ...
   0,   0,   0,   0,  1,   1,  3,  5, 10, 18, 33, 59, ...
   0,   0,   0,   1,  0,   2,  2,  5,  8, 15, 26, 46, ...
   0,   0,   1,  -1,  2,   0,  3,  3,  7, 11, 20, 34, ...
   0,   1,  -2,   3, -2,   3,  0,  4,  4,  9, 14, 24, ...
   1,  -3,   5,  -5,  5,  -3,  4,  0,  5,  5, 10, 16, ...
  -4,   8, -10,  10, -8,   7, -4,  5,  0,  6,  6, 17, ...
  12, -18,  20, -18, 15, -11,  9, -5,  6,  0,  7,  7, ...
  ...

Mathematica

a[n_] := Max[0, n - 2];
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];
Table[D[n, k], {n, 0, 11}, {k, 0, 11}]

Crossrefs

Essentially the same as A023444. Cf. A001477, A118425, A006478, A001629, A010049, A006367, A199969.

Sequence in context: A104661 A069782 A088480 * A061019 A028310 A097045

Adjacent sequences: A289204 A289205 A289206 * A289208 A289209 A289210

Keyword

nonn,less

Author

Jean-François Alcover and Paul Curtz, Jun 28 2017

Status

approved