The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A287317 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A287317

Number of 5-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages.
(history; published version)

#24 by Michael De Vlieger at Sun Jan 29 10:45:20 EST 2023

STATUS

reviewed

approved

#23 by Michel Marcus at Sun Jan 29 02:36:09 EST 2023

STATUS

proposed

reviewed

#22 by Michel Marcus at Sat Jan 28 15:36:06 EST 2023

STATUS

editing

proposed

#21 by Michel Marcus at Sat Jan 28 15:35:35 EST 2023

FORMULA

a(n) = Sum_{i+j+k+l+m=n, 0<=i,j,k,l,m<=n} multinomial(2n , [i ,i ,j ,j ,k ,k ,l ,l ,m ,m]). - Shel Kaphan, Jan 24 2023

STATUS

proposed

editing

Discussion

Sat Jan 28

15:36

Michel Marcus: @editors: is there a convention on how to write multinomials ?

#20 by Michel Marcus at Wed Jan 25 01:07:10 EST 2023

STATUS

editing

proposed

#19 by Michel Marcus at Wed Jan 25 01:07:05 EST 2023

MATHEMATICA

Table[Sum[(2 n)!/(i! j! k! l! (n-i-j-k-l)!)^2, {i, 0, n}, {j, 0, n-i}, {k, 0, n-i-j}, {l, 0, n-i-j-k}], {n, 0, 30}] - _(* _Shel Kaphan_, Jan 24 2023 *)

STATUS

proposed

editing

#18 by Shel Kaphan at Tue Jan 24 21:53:32 EST 2023

STATUS

editing

proposed

#17 by Shel Kaphan at Tue Jan 24 21:49:25 EST 2023

FORMULA

a(n) = Sum_{i+j+k+l+m<=n, 0<=i,j,k,l,m<=n} multinomial(2n [i i j j k k l l m m]). - Shel Kaphan, Jan 24 2023

#16 by Shel Kaphan at Tue Jan 24 21:45:39 EST 2023

FORMULA

a(n) = Sum_{i+j+k+l+m<=n, 0<=i,j,k,l,m<=n} multinomial(2n [i i j j k k l l m m] ). - _Shel Kaphan_, Jan 24 2023

MATHEMATICA

Table[Sum[(2 n)!/(i! j! k! l! (n-i-j-k-l)!)^2, {i, 0, n}, {j, 0, n-i}, {k, 0, n-i-j}, {l, 0, n-i-j-k}], {n, 0, 30}] - _Shel Kaphan_, Jan 24 2023

Discussion

Tue Jan 24

21:47

Shel Kaphan: Added formula and corresponding Mathematica code

#15 by Shel Kaphan at Tue Jan 24 21:42:56 EST 2023

FORMULA

a(n) = Sum_{i+j+k+l+m<=n, 0<=i,j,k,l,m<=n} multinomial(2n [i i j j k k l l m m] )

MATHEMATICA

Table[Sum[(2 n)!/(i! j! k! l! (n-i-j-k-l)!)^2, {i, 0, n}, {j, 0, n-i}, {k, 0, n-i-j}, {l, 0, n-i-j-k}], {n, 0, 30}]

STATUS

approved

editing