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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A171486 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A033321.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 6, 5, 3, 1, 21, 16, 9, 4, 1, 79, 58, 31, 14, 5, 1, 311, 224, 117, 52, 20, 6, 1, 1265, 900, 465, 205, 80, 27, 7, 1, 5275, 3720, 1910, 840, 330, 116, 35, 8, 1, 22431, 15713, 8034, 3532, 1396, 501, 161, 44, 9, 1, 96900, 67522, 34419, 15136, 6015, 2190
Offset: 0

Views

Author

Philippe Deléham, Dec 09 2009

Keywords

Comments

Equal to B*A065600 = A171224*B where B = A007318 ; equal to B*A039598*B^(-2).

Examples

			Triangle begins :
1
1, 1
2, 2, 1
6, 5, 3, 1
21, 16, 9, 4, 1
79, 58, 31, 14, 5, 1
311, 224, 117, 52, 20, 6, 1

Crossrefs

Cf. A171224, A104259, A091965

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A117641(n), A033321(n), A007317(n+1), A002212(n+1), A026378(n+1) for x = -1, 0, 1, 2, 3 respectively.
T(n,k) = T(n-1,k-1) + T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*2^i. - Philippe Deléham, Feb 23 2012

A236420 Riordan array (1/(1-3*x), (1-3*x-sqrt(1-6*x+5*x^2))/(2*x)).

Original entry on oeis.org

1, 3, 1, 9, 6, 1, 27, 28, 9, 1, 81, 120, 56, 12, 1, 243, 497, 300, 93, 15, 1, 729, 2034, 1490, 594, 139, 18, 1, 2187, 8321, 7098, 3411, 1029, 194, 21, 1, 6561, 34248, 33026, 18360, 6692, 1632, 258, 24, 1, 19683, 142331, 151686, 94798, 40068, 11846, 2430, 331, 27, 1
Offset: 0

Views

Author

Philippe Deléham, Jan 25 2014

Keywords

Comments

T(n,0) = 3^n = A000244(n).
T(n,2) = A002212(n+1) - 3^n.
T(n+1,n) = 3n+3 = A008585(n+1).
T(n+2,n) = (9*n^2+29*n+18)/2.

Examples

			Triangle begins:
1;
3, 1;
9, 6, 1;
27, 28, 9, 1;
81, 120, 56, 12, 1;
243, 497, 300, 93, 15, 1;
729, 2034, 1490, 594, 139, 18, 1

Crossrefs

Cf. Similar sequences: A091965, A110165

Formula

T(n,0) = 3*T(n-1,0), T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + T(n-1,k+1) for k>0, T(n,k) = 0 if k<0 or if k>n, T(0,0) = 1.
Previous Showing 31-32 of 32 results.

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

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