The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by DELEHAM Philippe (See also DELEHAM Philippe's wiki page)

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

A109466

Riordan array (1, x(1-x)).
(history; published version)

#18 by DELEHAM Philippe at Fri Feb 22 00:22:49 EST 2013

STATUS

editing

proposed

#17 by DELEHAM Philippe at Fri Feb 22 00:22:40 EST 2013

FORMULA

Sum_[k, 0<=k<=n}T(n,k)*x^(n-k) = F(n+1,-x) where F(n,x)is the n-th Fibonacci polynomial in x defined in A011973. - From DELEHAM Philippe, Feb 22 2013

STATUS

approved

editing

A055585

Second column of triangle A055584.
(history; published version)

#16 by DELEHAM Philippe at Wed Feb 20 23:52:00 EST 2013

STATUS

editing

proposed

#15 by DELEHAM Philippe at Wed Feb 20 23:51:46 EST 2013

COMMENTS

Convolution of A001792 with itself. - DELEHAM Philippe, Feb 21 2013

STATUS

approved

editing

A221179

A convolution triangle of numbers obtained from A146559.
(history; published version)

#12 by DELEHAM Philippe at Wed Feb 20 21:54:29 EST 2013

STATUS

editing

proposed

#11 by DELEHAM Philippe at Wed Feb 20 21:54:18 EST 2013

NAME

allocated for DELEHAM PhilippeA convolution triangle of numbers obtained from A146559.

DATA

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, -2, 1, 3, 1, 0, -4, -4, 3, 4, 1, 0, -4, -12, -5, 6, 5, 1, 0, 0, -16, -24, -4, 10, 6, 1, 0, 8, -4, -42, -39, 0, 15, 7, 1, 0, 16, 32, -24, -88, -55, 8, 21, 8, 1, 0, 16, 80, 72, -80

OFFSET

0,9

COMMENTS

Triangle T(n,k) given by (0, 1, -1, 2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

FORMULA

G.f. for the k-th column: ((x-x^2)/(1-2*x+2*x^2))^k.

G.f.: (1-2*x+2*x^2)/(1-2*x+2*x^2-x*y+x^2*y).

T(n,k) = 2*T(n-1,k) + T(n-1,k-1) - 2*T(n-2,k) - T(n-2,k-1), T(0,0)=1, T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.

T(n,k) = (-1)^(n-k)*A181472(n-1,k-1) for n>0 and k>0.

T(n,1) = A146559(n-1).

T(n+1,n) = n = A001477(n).

T(n+2,n) = (n^2-n)/2 = A161680(n).

Sum_{k, 0<=k<=n} T(n,k) = A057682(n) for n>0.

EXAMPLE

Triangle begins:

1

0, 1

0, 1, 1

0, 0, 2, 1

0, -2, 1, 3, 1

0, -4, -4, 3, 4, 1

0, -4, -12, -5, 6, 5, 1

0, 0, -16, -24, -4, 10, 6, 1

CROSSREFS

Cf. A030523, A104597, A181472, A220399

KEYWORD

allocated

sign,tabl

AUTHOR

DELEHAM Philippe, Feb 20 2013

STATUS

approved

editing

#10 by DELEHAM Philippe at Wed Feb 20 21:54:18 EST 2013

NAME

allocated for DELEHAM Philippe

KEYWORD

recycled

allocated

A220399

A convolution triangle of numbers obtained from A057682.
(history; published version)

#12 by DELEHAM Philippe at Wed Feb 20 21:29:17 EST 2013

STATUS

editing

proposed

#11 by DELEHAM Philippe at Wed Feb 20 21:29:03 EST 2013

COMMENTS

Triangle T(n,k) given by (0, 2, -1/2, 13/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

CROSSREFS

Cf. A030523, A057682, A104597

STATUS

proposed

editing

A104597

Triangle T read by rows: inverse of Motzkin triangle A097609.
(history; published version)

#19 by DELEHAM Philippe at Wed Feb 20 17:33:47 EST 2013

STATUS

editing

proposed