The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A261358 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A261358

Pentatope of coefficients in expansion of (1 + x + y + 2*z)^n.
(history; published version)

#42 by Charles R Greathouse IV at Sat Aug 29 00:17:47 EDT 2015

STATUS

editing

approved

#41 by Charles R Greathouse IV at Sat Aug 29 00:17:38 EDT 2015

KEYWORD

nonn,tabf,walk,changed,less

STATUS

proposed

editing

#40 by Michel Marcus at Mon Aug 24 05:08:12 EDT 2015

STATUS

editing

proposed

#39 by Michel Marcus at Mon Aug 24 05:08:05 EDT 2015

KEYWORD

nonn,tabf,walk,changed

STATUS

proposed

editing

#38 by Jon E. Schoenfield at Sun Aug 23 23:42:47 EDT 2015

STATUS

editing

proposed

#37 by Jon E. Schoenfield at Sun Aug 23 23:42:43 EDT 2015

COMMENTS

The sum of the antidiagonals of each triangle in each slice gives A261357. -_ _Dimitri Boscainos_, Aug 21 2015

FORMULA

T(i+1,j,k,l) = 2*T(i,j-1,k-1,l-1) + T(i,j-1,k-1,l) + T(i,j-1,k,l) + T(i,j,k,l); a(i,j,k,-1)=0,...; a(0,0,0,0)=1.

STATUS

proposed

editing

#36 by Dimitri Boscainos at Fri Aug 21 18:27:58 EDT 2015

STATUS

editing

proposed

#35 by Dimitri Boscainos at Fri Aug 21 18:27:49 EDT 2015

COMMENTS

The sum of the antidiagonals of each triangle in each slice gives A261357. -Dimitri Boscainos, Aug 21 2015

CROSSREFS

Cf. A000351, A189225, A261357, A261359, A261360.

STATUS

proposed

editing

#34 by Wesley Ivan Hurt at Fri Aug 21 11:07:56 EDT 2015

STATUS

editing

proposed

#33 by Wesley Ivan Hurt at Fri Aug 21 11:07:10 EDT 2015

FORMULA

T(i+1,j,k,l) = 2*T(i,j-1,k-1,l-1)+T(i,j-1,k-1,l)+T(i,j-1,k,l)+T(i,j,k,l); a(i,j,k,-1)=0,...; a(0,0,0,0)=1.

T(n,i,j,k) = 2^k*binomial(n,i)*binomial(i,j)*binomial(j,k). - Dimitri Boscainos, Aug 21 2015

CROSSREFS

Cf. A000351, A189225.

STATUS

proposed

editing