The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A290286

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

A290286

Determinant of circulant matrix of order 4 with entries in the first row (-1)^j*Sum_{k>=0}(-1)^k*binomial(n, 4*k+j), j=0,1,2,3.
(history; published version)

#30 by Alois P. Heinz at Mon Apr 12 08:32:15 EDT 2021

STATUS

proposed

approved

#29 by F. Chapoton at Mon Apr 12 07:57:12 EDT 2021

STATUS

editing

proposed

#28 by F. Chapoton at Mon Apr 12 07:56:53 EDT 2021

PROG

from sympy import binomial, floor

def mj(j, n): return (-1)**j*sum([(-1)**k*binomial(n, 4*k + j) for k in range(floor(n//4) + 1)])

m=Matrix(4, 4, [0]*16lambda i, j: mj((i-j)%4, n))

for j in range(4):m[0, j]=mj(j, n)

for j in range(1, 4):m[1, j]=m[0, j - 1]

m[1, 0]=m[0, 3]

for j in range(1, 4):m[2, j] = m[1, j - 1]

m[2, 0]=m[1, 3]

for j in range(1, 4):m[3, j] = m[2, j - 1]

m[3, 0]=m[2, 3]

print map([a, (n) for n in range(22)]) # Indranil Ghosh, Jul 31 2017

STATUS

approved

editing

Discussion

Mon Apr 12

07:57

F. Chapoton: adapt py code to py3, and simplify

#27 by N. J. A. Sloane at Sat Dec 07 12:33:53 EST 2019

PROG

print map(a, xrangerange(22)) # Indranil Ghosh, Jul 31 2017

Discussion

Sat Dec 07

12:33

OEIS Server: https://oeis.org/edit/global/2838

#26 by N. J. A. Sloane at Sat Dec 07 12:18:29 EST 2019

PROG

def mj(j, n): return (-1)**j*sum([(-1)**k*binomial(n, 4*k + j) for k in xrangerange(floor(n/4) + 1)])

for j in xrangerange(4):m[0, j]=mj(j, n)

for j in xrangerange(1, 4):m[1, j]=m[0, j - 1]

for j in xrangerange(1, 4):m[2, j] = m[1, j - 1]

for j in xrangerange(1, 4):m[3, j] = m[2, j - 1]

Discussion

Sat Dec 07

12:18

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

#25 by Bruno Berselli at Thu Aug 09 10:23:16 EDT 2018

STATUS

reviewed

approved

#24 by Joerg Arndt at Thu Aug 09 09:56:20 EDT 2018

STATUS

proposed

reviewed

#23 by Jean-François Alcover at Thu Aug 09 09:40:51 EDT 2018

STATUS

editing

proposed

#22 by Jean-François Alcover at Thu Aug 09 09:40:46 EDT 2018

MATHEMATICA

ro[n_] := Table[Sum[(-1)^(j+k) Binomial[n, 4k+j], {k, 0, n/4}], {j, 0, 3}];

M[n_] := Table[RotateRight[ro[n], m], {m, 0, 3}];

a[n_] := Det[M[n]];

Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Aug 09 2018 *)

STATUS

approved

editing

#21 by Michel Marcus at Mon Jul 31 11:36:59 EDT 2017

STATUS

reviewed

approved