The On-Line Encyclopedia of Integer Sequences (OEIS)

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A208748

Triangle of coefficients of polynomials v(n,x) jointly generated with A208747; see the Formula section.
(history; published version)

#17 by R. J. Mathar at Tue Aug 11 13:56:35 EDT 2015

STATUS

editing

approved

#16 by R. J. Mathar at Tue Aug 11 13:56:28 EDT 2015

FORMULA

G.f.: (-1+x-2*x*y)*x*y/(-1+x+2*x*y-2*x^2*y+4*x^2*y^2). - R. J. Mathar, Aug 11 2015

STATUS

approved

editing

#15 by R. J. Mathar at Tue Aug 11 13:56:06 EDT 2015

STATUS

editing

approved

#14 by R. J. Mathar at Tue Aug 11 13:56:00 EDT 2015

FORMULA

G.f.: (-1+x-2*x*y)/(-1+x+2*x*y-2*x^2*y+4*x^2*y^2). - R. J. Mathar, Aug 11 2015

STATUS

approved

editing

#13 by N. J. A. Sloane at Sun Sep 08 19:59:31 EDT 2013

COMMENTS

As triangle T(n,k) with 0<=k<=n, it is (0, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (4, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham, _, Mar 14 2012

FORMULA

T(n,k) = 2^k*A208343(n,k). - _Philippe Deléham, _, Mar 05 2012

T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) + 4*T(n-2,k-2), T(1,0) = 1, T(2,0) = T(3,0) = 0, T(2,1) = 4, T(3,1) = 2, T(3,2) = 12, T(n,k) = 0 if k<0 or if k>=n. - _Philippe Deléham, _, Mar 14 2012

Discussion

Sun Sep 08

19:59

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

#12 by N. J. A. Sloane at Fri Feb 22 14:40:30 EST 2013

COMMENTS

As triangle T(n,k) with 0<=k<=n, it is (0, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (4, -1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - DELEHAM Philippe, Deléham, Mar 14 2012

FORMULA

T(n,k) = 2^k*A208343(n,k). - DELEHAM Philippe, Deléham, Mar 05 2012

T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) + 4*T(n-2,k-2), T(1,0) = 1, T(2,0) = T(3,0) = 0, T(2,1) = 4, T(3,1) = 2, T(3,2) = 12, T(n,k) = 0 if k<0 or if k>=n. - DELEHAM Philippe, Deléham, Mar 14 2012

Discussion

Fri Feb 22

14:40

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

#11 by Russ Cox at Fri Mar 30 18:58:14 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Mar 02 2012

Discussion

Fri Mar 30

18:58

OEIS Server: https://oeis.org/edit/global/285

#10 by T. D. Noe at Wed Mar 14 13:04:09 EDT 2012

STATUS

proposed

approved

#9 by DELEHAM Philippe at Wed Mar 14 04:49:18 EDT 2012

STATUS

editing

proposed

#8 by DELEHAM Philippe at Wed Mar 14 04:49:08 EDT 2012

COMMENTS

FORMULA

T(n,k) = T(n-1,k) + 2*T(n-1,k-1) - 2*T(n-2,k-1) + 4*T(n-2,k-2), T(1,0) = 1, T(2,0) = T(3,0) = 0, T(2,1) = 4, T(3,1) = 2, T(3,2) = 12, T(n,k) = 0 if k<0 or if k>=n. - DELEHAM Philippe, Mar 14 2012

STATUS

approved

editing