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Revision History for A165241 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,1,0,0,0,0,0,0,0,...] DELTA [1,0,1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938.
(history; published version)
#22 by N. J. A. Sloane at Wed Jan 18 22:19:50 EST 2017
STATUS

proposed

approved

#21 by Tom Copeland at Tue Jan 17 14:16:23 EST 2017
STATUS

editing

proposed

#20 by Tom Copeland at Sun Jan 15 13:06:12 EST 2017
COMMENTS

Appear to be the The sums of each column of A117317 with its subsequent column, treated as a lower triangular matrix with an initial null column attached, or, equivalently, the products of the row polynomials p(n,y) of A117317 with (1+y) with the initial first row below added to the final result. The reversal of A117317 is A056242 with several combinatorial interpretations. - Tom Copeland, Jan 08 2017

FORMULA

G.f.: (1-(1+y)*x)/(1-2(1+y)*x+(y+y^2)*x^2). - Philippe Deléham, Dec 19 2011

EXTENSIONS

O.g.f. corrected by Tom Copeland, Jan 15 2017

STATUS

approved

editing

#19 by N. J. A. Sloane at Sat Jan 14 07:55:31 EST 2017
STATUS

proposed

approved

#18 by Tom Copeland at Mon Jan 09 16:19:46 EST 2017
STATUS

editing

proposed

#17 by Tom Copeland at Mon Jan 09 15:12:15 EST 2017
COMMENTS

Appear to be the sums of each column of A117317 with its subsequent column , treated as a lower triangular matrix with an initial null columns column attached to both sides, , or, equivalently, the products of the row polynomials p(n,y) of A117317 with (1+y) with the initial first row below added to the final result. The reversal of A117317 is A056242 with several combinatorial interpretations. - Tom Copeland, Jan 08 2017

CROSSREFS
#16 by Tom Copeland at Mon Jan 09 13:43:36 EST 2017
COMMENTS

Appear to be the sums of each column of A117317 with its subsequent column treated as a lower triangular matrix with null columns attached to both sides, or, equivalently, the products of the row polynomials p(n,y) of A117317 with (1+xy) with the initial first row below added to the final result. - Tom Copeland, Jan 08 2017

Discussion
Mon Jan 09
14:17
Tom Copeland: There appears to be a factor of 2 missing in the denominator of the o.g.f. here. It should read 1 - 2( 1+y) x + y (1+y) x^2. My math app is down. Could someone please check the expansion? If I'm correct then my conjecture is true.
#15 by Tom Copeland at Mon Jan 09 13:34:59 EST 2017
COMMENTS

Appears Appear to be the sums of each column of A117317 with the its subsequent column of A117317 treated as a lower triangular matrix with null columns attached to both sides, or, equivalently, the products of the row polynomials of A117317 with (1+x). - Tom Copeland, Jan 08 2017

#14 by Tom Copeland at Mon Jan 09 13:27:59 EST 2017
COMMENTS

Appears to be the sum sums of adjacent columns each column with the subsequent column of A117317 treated as a lower triangular matrix with null columns attached to both sides. - Tom Copeland, Jan 08 2017

STATUS

proposed

editing

#13 by Jon E. Schoenfield at Mon Jan 09 13:18:58 EST 2017
STATUS

editing

proposed

Discussion
Mon Jan 09
13:22
Tom Copeland: All adjacent columns with null columns attached to either side of the lower triangular matrix. I suppose if you can't see this quickly by inspection then I should explain more.