The On-Line Encyclopedia of Integer Sequences (OEIS)

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A147703

Triangle [1,1,1,0,0,0,...] DELTA [1,0,0,0,...] with Deléham DELTA defined in A084938.
(history; published version)

#27 by Vaclav Kotesovec at Fri May 28 07:58:37 EDT 2021

STATUS

proposed

approved

#26 by Kevin Ryde at Fri May 28 07:31:51 EDT 2021

STATUS

editing

proposed

#25 by Kevin Ryde at Fri May 28 07:31:30 EDT 2021

CROSSREFS

Cf. A062110, A007318, A062110, A206800, A001519, A321620.

STATUS

approved

editing

Discussion

Fri May 28

07:31

Kevin Ryde: Duplicate crossref.

#24 by Peter Luschny at Sun Jan 26 19:09:58 EST 2020

STATUS

proposed

approved

#23 by Peter Luschny at Sun Jan 26 18:31:16 EST 2020

STATUS

editing

proposed

#22 by Peter Luschny at Sun Jan 26 18:30:31 EST 2020

COMMENTS

Row sums are A006012. Diagonal sums are A147704. Equal to A062110*A007318 when A062110 is regarded as a triangle read by rows.

FORMULA

The Riordan square of the odd indexed Fibonacci numbers A001519. - Peter Luschny, Jan 26 2020

MAPLE

# The function RiordanSquare is defined in A321620:

RiordanSquare(1 / (1 - x / (1 - x / (1 - x))), 10); # Peter Luschny, Jan 26 2020

CROSSREFS

CfRow sums are A006012. A206800Diagonal sums are A147704.

Cf. A062110, A007318, A062110, A206800, A001519, A321620.

STATUS

approved

editing

#21 by Alois P. Heinz at Mon Jan 20 17:02:01 EST 2020

STATUS

proposed

approved

#20 by Jon E. Schoenfield at Mon Jan 20 15:58:54 EST 2020

STATUS

editing

proposed

#19 by Jon E. Schoenfield at Mon Jan 20 15:58:52 EST 2020

NAME

Triangle [1,1,1,0,0,0,...] DELTA [1,0,0,0,.....] with Deléham DELTA defined in A084938.

FORMULA

Sum_{k, =0<=k<=..n} T(n,k)*x^k = A152239(n), A152223(n), A152185(n), A152174(n), A152167(n), A152166(n), A152163(n), A000007(n), A001519(n), A006012(n), A081704(n), A082761(n), A147837(n), A147838(n), A147839(n), A147840(n), A147841(n), for x = -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8 respectively . - Philippe Deléham, Dec 01 2008

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k) - T(n-2,k-1), for n > 1. - Philippe Deléham, Feb 12 2012

EXAMPLE

1,;

1, 1,;

2, 3, 1,;

5, 9, 5, 1,;

13, 27, 20, 7, 1,;

34, 80, 73, 35, 9, 1,;

89, 234, 252, 151, 54, 11, 1;

CROSSREFS

Cf. A206800.

STATUS

approved

editing

#18 by Michel Marcus at Sat Mar 11 03:44:22 EST 2017

STATUS

reviewed

approved