The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A207608

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A207608

Triangle of coefficients of polynomials u(n,x) jointly generated with A207609; see the Formula section.
(history; published version)

#25 by Peter Luschny at Mon Apr 13 06:24:12 EDT 2020

STATUS

reviewed

approved

#24 by Michel Marcus at Mon Apr 13 05:15:10 EDT 2020

STATUS

proposed

reviewed

#23 by Indranil Ghosh at Mon Apr 13 04:00:09 EDT 2020

STATUS

editing

proposed

Discussion

Mon Apr 13

05:15

Michel Marcus: I use https://sagecell.sagemath.org/ to check

#22 by Indranil Ghosh at Mon Apr 13 03:59:27 EDT 2020

PROG

for n in range(1, 13): print (a(n) ) # Indranil Ghosh, May 28 2017

STATUS

proposed

editing

Discussion

Mon Apr 13

04:00

Indranil Ghosh: I am sorry Michel. This should be Python 3. Thanks!

#21 by Indranil Ghosh at Mon Apr 13 03:56:59 EDT 2020

STATUS

editing

proposed

Discussion

Mon Apr 13

03:57

Michel Marcus: SyntaxError: invalid syntax

#20 by Indranil Ghosh at Mon Apr 13 03:56:52 EDT 2020

PROG

from sympy.abc import x

STATUS

approved

editing

#19 by N. J. A. Sloane at Sat Dec 07 12:18:26 EST 2019

PROG

for n in xrangerange(1, 13): print a(n) # Indranil Ghosh, May 28 2017

Discussion

Sat Dec 07

12:18

OEIS Server: https://oeis.org/edit/global/2837

#18 by Susanna Cuyler at Tue Nov 06 21:19:50 EST 2018

STATUS

proposed

approved

#17 by Jon E. Schoenfield at Tue Nov 06 18:59:50 EST 2018

STATUS

editing

proposed

#16 by Jon E. Schoenfield at Tue Nov 06 18:59:47 EST 2018

FORMULA

u(n,x) = u(n-1,x) + v(n-1,x),

v(n,x) = 2x*u(n-1,x) + (x+1)v(n-1,x),

As triangle T(n,k), 0 <= k <= n :

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

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

Sum_{k, =0<=k<=..n} T(n,k)*x^k = A000027(n+1), A025192(n), A001077(n), A180038(n) for x = 0, 1, 2, 3 respectively. (End)

EXAMPLE

1;

2;

3..., 3;

4..., 11..., 3;

5..., 26..., 20..., 3;

Triangle (2, -1/2, 1/2, 0, 0, 0, 0, ...) DELTA (0, 3/2, -1/2, 0, 0, 0, 0, ...) begins :

1;

2, 0;

3, 3, 0;

4, 11, 3, 0;

5, 26, 20, 3, 0;

6, 50, 74, 29, 3, 0;

7, 85, 204, 149, 38, 3, 0;

... - Philippe Deléham, Mar 03 2012

STATUS

proposed

editing