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.

Showing 1-2 of 2 results.

A239101 Riordan array read by rows, corresponding to array in A180562.

Original entry on oeis.org

1, 2, 1, 4, 2, 1, 10, 5, 2, 1, 26, 13, 6, 2, 1, 70, 35, 16, 7, 2, 1, 192, 96, 45, 19, 8, 2, 1, 534, 267, 126, 56, 22, 9, 2, 1, 1500, 750, 357, 160, 68, 25, 10, 2, 1, 4246, 2123, 1016, 463, 198, 81, 28, 11, 2, 1, 12092, 6046, 2907, 1337, 586, 240, 95, 31
Offset: 0

Views

Author

N. J. A. Sloane, Mar 25 2014

Keywords

Comments

Take lower triangle of square array in A180562, read from right to left.
Row sums are in A225034. - Philippe Deléham, Mar 25 2014
Riordan array (f(x), (f(x)-1)/(2*f(x))) where f(x) = sqrt((1+x)/(1-3*x)). - Philippe Deléham, Mar 25 2014

Examples

			Triangle begins:
1
2 1
4 2 1
10 5 2 1
26 13 6 2 1
70 35 16 7 2 1
192 96 45 19 8 2 1
...
192 = 2*96, 96 = 70 - 35 + 16 + 45, 45 = 35 - 16 + 7 + 19, etc. - _Philippe Deléham_, Mar 25 2014
Production matrix is:
2, 1
0, 0, 1
2, 1, 0, 1
2, 1, 1, 0, 1
2, 1, 1, 1, 0, 1
2, 1, 1, 1, 1, 0, 1
2, 1, 1, 1, 1, 1, 0, 1
2, 1, 1, 1, 1, 1, 1, 0, 1
... _Philippe Deléham_, Sep 15 2014

Links

Crossrefs

Cf. A180562.
Cf. T(n,0) = A025565(n+1), T(n+1,1) = A005773(n+1), T(n+2,2) = A005717(n+1), A225034 (Row sums). - Philippe Deléham, Mar 25 2014

Formula

T(0,0) = 1, T(n,0) = 2*T(n,1) for n>0, T(n,k) = T(n-1,k-1) - T(n-1,k) + T(n-1,k+1) + T(n,k+1) for k>0, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 25 2014

Extensions

More terms from Philippe Deléham, Mar 25 2014

A124445 Expansion of 1/(1-x-x*y+x^2*y-x^3*y^2).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 5, 4, 1, 1, 1, 5, 7, 8, 5, 1, 1, 1, 6, 9, 13, 12, 6, 1, 1, 1, 7, 11, 19, 22, 17, 7, 1, 1, 1, 8, 13, 26, 35, 35, 23, 8, 1, 1, 1, 9, 15, 34, 51, 61, 53, 30, 9, 1
Offset: 0

Views

Author

Paul Barry, Nov 01 2006

Keywords

Comments

Row sums are A107293(n+4). Diagonal sums are A005314(n+1).
Reversal of A124279. T(2n,n) is A002426. - Paul Barry, Nov 01 2006

Examples

			Triangle begins:
1,
1, 1,
1, 1, 1,
1, 1, 2, 1,
1, 1, 3, 3, 1,
1, 1, 4, 5, 4, 1,
1, 1, 5, 7, 8, 5, 1,
1, 1, 6, 9, 13, 12, 6, 1,
1, 1, 7, 11, 19, 22, 17, 7, 1

Crossrefs

Cf. A180562.

Formula

Number triangle T(n,k)=sum{j=0..n, C(j,k-j)*C(n-k,k-j)}*[k<=n];
T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) + T(n-3,k-2), T(0,0) = T(1,0) = T(1,1) = T(2,0) = T(2,1) = T(2,2) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Mar 25 2014
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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