cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

Views

Author

Philippe Deléham, Feb 29 2024

Keywords

Examples

			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.

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.
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