The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A171509 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A171509

Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126931.
(history; published version)

#14 by Joerg Arndt at Sat Oct 12 01:40:32 EDT 2024

STATUS

proposed

approved

#13 by Jason Yuen at Sat Oct 12 00:09:25 EDT 2024

STATUS

editing

proposed

#12 by Jason Yuen at Sat Oct 12 00:09:21 EDT 2024

CROSSREFS

Cf. A053121, A054336, A096164, A171505.

#11 by Jason Yuen at Sat Oct 12 00:04:48 EDT 2024

FORMULA

Sum_[{k, =0<=k<=..n} T(n,k)*x^k = A126930(n), A126120(n), A001405(n), A054341(n), A126931(n) for x = -4, -3, -2, -1, 0 respectively.

T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + sum_Sum_{i, i>=0} T(n-1,k+1+i)*(-3)^i. - Philippe Deléham, Feb 23 2012

EXAMPLE

Triangle begins : 1 ; 3,1 ; 10,6,1 ; 33,29,9,1 ; 110,126,57,12,1 ; ...

1 ;

3,1 ;

10,6,1 ;

33,29,9,1 ;

110,126,57,12,1 ; ...

STATUS

approved

editing

#10 by N. J. A. Sloane at Sun Sep 08 19:59:25 EDT 2013

FORMULA

T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*(-3)^i. - _Philippe Deléham, _, Feb 23 2012

Discussion

Sun Sep 08

19:59

OEIS Server: https://oeis.org/edit/global/1941

#9 by N. J. A. Sloane at Sun Sep 08 13:31:52 EDT 2013

AUTHOR

_Philippe DELEHAM_, Deléham_, Dec 10 2009

Discussion

Sun Sep 08

13:31

OEIS Server: https://oeis.org/edit/global/1938

#8 by N. J. A. Sloane at Fri Feb 22 14:39:41 EST 2013

FORMULA

T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*(-3)^i. - DELEHAM Philippe, Deléham, Feb 23 2012

Discussion

Fri Feb 22

14:39

OEIS Server: https://oeis.org/edit/global/1863

#7 by Russ Cox at Sat Mar 31 10:28:09 EDT 2012

AUTHOR

_Philippe DELEHAM (kolotoko(AT)wanadoo.fr), _, Dec 10 2009

Discussion

Sat Mar 31

10:28

OEIS Server: https://oeis.org/edit/global/535

#6 by Bruno Berselli at Fri Feb 24 06:58:54 EST 2012

STATUS

editing

approved

#5 by Bruno Berselli at Fri Feb 24 06:58:51 EST 2012

FORMULA

T(n,k) = T(n-1,k-1) + 3*T(n-1,k) + Sum_sum_{i, i>=0} T(n-1,k+1+i)*(-3)^i. - DELEHAM Philippe, Feb 23 2012

STATUS

approved

editing