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.

A206819 Riordan array (1/(1-10*x-10*x^2), x/(1-10*x-10*x^2)).

Original entry on oeis.org

1, 10, 1, 90, 20, 1, 800, 280, 30, 1, 7100, 3400, 570, 40, 1, 63000, 38300, 8800, 960, 50, 1, 559000, 412000, 120600, 18000, 1450, 60, 1, 4960000, 4296000, 1530000, 291000, 32000, 2040, 70, 1
Offset: 0

Views

Author

Philippe Deléham, Feb 12 2012

Keywords

Comments

Row sums are A000042(n+1).
Subtriangle of triangle given by (0, 10, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

Examples

			Triangle begins :
1
10, 1
90, 20, 1
800, 280, 30, 1
7100, 3400, 570, 40, 1
63000, 38300, 8800, 960, 50, 1
559000, 412000, 120600, 18000, 1450, 60, 1
4960000, 4296000, 1530000, 291000, 32000, 2040, 70, 1
Triangle (0, 10, -1, 1, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) begins :
1
0, 1
0, 10, 1
0, 90, 20, 1
0, 800, 280, 30, 1
0, 7100, 3400, 570, 40, 1 ...

Crossrefs

Cf. A101950, A178865,

Formula

T(n,k) = 10*T(n-1,k) - 10*T(n-2,k) + T(n-1,k-1).
G.f.: 1/(1-10*x+10*x^2-y*x).
Sum_{k, 0<=k} T(n,k)*x^k = A178869(n+1), A057086(n), A000042(n+1) for x = -1, 0, 1 respectively.

A178870 Signed Delannoy triangle convolved with 10^n.

Original entry on oeis.org

1, 10, -1, 100, -30, 1, 1000, -500, 50, -1, 10000, -7000, 1300, -70, 1, 100000, -90000, 25000, -2500, 90, -1, 1000000, -1100000, 410000, -63000, 4100, -110, 1, 10000000, -13000000, 6100000, -1290000, 129000, -6100, 130, -1
Offset: 0

Views

Author

Mark Dols, Jun 20 2010

Keywords

Comments

Row sums give A178869

Examples

			Triangle begins:
1
10, -1
100, -30, 1
1000, -500, 50, -1
10000, -7000, 1300, -70, 1
100000, -90000, 25000, -2500, 90, -1
1000000, -1100000, 410000, -63000, 4100, -110, 1
10000000, -13000000, 6100000, -1290000, 129000, -6100, 130, -1

Crossrefs

Cf. A008288, A165293, A178865, A178869

Formula

T(n,k) = A008288(n,k)*(-10)^(n-k)*(-1)^n, A008288 seen as a triangle read by rows. - Philippe Deléham, Feb 27 2013

Extensions

More terms from Philippe Deléham, Feb 27 2013
Showing 1-2 of 2 results.

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

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