A370174 Triangle read by rows: Riordan array (1/(1 - x), x*(1 + x)/(1 - x - x^2)).

1, 1, 1, 1, 3, 1, 1, 6, 5, 1, 1, 11, 15, 7, 1, 1, 19, 37, 28, 9, 1, 1, 32, 82, 87, 45, 11, 1, 1, 53, 170, 234, 169, 66, 13, 1, 1, 87, 337, 573, 535, 291, 91, 15, 1, 1, 142, 647, 1314, 1511, 1061, 461, 120, 17, 1, 1, 231, 1213, 2871, 3933, 3398, 1904, 687, 153, 19, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1), T(n,0) = 1, T(n,k) = 0 if k > n.

Sum_{k = 0..n} T(n,k)* x^k = A000012(n), A057960(n), A196472(n+1), A218988(n-1) for x = 0, 1, 2, 3 respectively.

Example

Triangle T(n,k) begins:
      k=0   1   2   3   4   5    6
  n=0:  1;
  n=1:  1,  1;
  n=2:  1,  3,  1;
  n=3:  1,  6,  5,  1;
  n=4:  1, 11, 15,  7,  1;
  n=5:  1, 19, 37, 28,  9,  1;
  n=6:  1, 32, 82, 87, 45, 11,  1;
  ...
87 = 28 + 37 + 7 + 15.

Crossrefs

Cf. A000012 (column k=0), A000384, A001911, A005408.

Cf. A057960 (row sums), A196472, A218988.

Sequence in context: A145904 A273350 A328083 * A278132 A203950 A273349

Adjacent sequences: A370171 A370172 A370173 * A370175 A370176 A370177

Keyword

nonn,tabl,easy

Author

Philippe Deléham, Feb 29 2024

Status

approved