The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A280059 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A280059

Number of 2 X 2 matrices having all elements in {-n,..,0,..,n} with determinant = permanent.
(history; published version)

#11 by Charles R Greathouse IV at Tue Oct 18 15:31:04 EDT 2022

STATUS

editing

approved

#10 by Charles R Greathouse IV at Tue Oct 18 15:31:02 EDT 2022

KEYWORD

nonn,easy

STATUS

approved

editing

#9 by N. J. A. Sloane at Sun Dec 25 02:45:10 EST 2016

STATUS

proposed

approved

#8 by G. C. Greubel at Sun Dec 25 01:45:12 EST 2016

STATUS

editing

proposed

#7 by G. C. Greubel at Sun Dec 25 01:44:50 EST 2016

LINKS

<a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

FORMULA

a(x-1n) = 16*(xn+1)^3) - 28*(xn+1)^2) + 16*x(n+1) - 3 for xn>0.

From G. C. Greubel, Dec 25 2016: (Start)

G.f.: (1 + 41*x + 51*x^2 + 3*x^3)/(1 - x)^4.

E.g.f.: (1 + 44*x + 68*x^2 + 16*x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

MATHEMATICA

Table[16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 45, 225, 637}, 50] (* G. C. Greubel, Dec 25 2016 *)

PROG

(PARI) for(n=0, 50, print1(16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, ", ")) \\ G. C. Greubel, Dec 25 2016

STATUS

proposed

editing

#6 by Indranil Ghosh at Sun Dec 25 01:34:15 EST 2016

STATUS

editing

proposed

#5 by Indranil Ghosh at Sun Dec 25 01:33:16 EST 2016

PROG

for i in range(0, 2011001):

STATUS

proposed

editing

#4 by Indranil Ghosh at Sun Dec 25 01:05:11 EST 2016

STATUS

editing

proposed

#3 by Indranil Ghosh at Sun Dec 25 01:00:10 EST 2016

LINKS

Indranil Ghosh, <a href="/A280059/b280059.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(x-1)=16*(x^3)-28*(x^2)+16*x-3 for x>0.

#2 by Indranil Ghosh at Sun Dec 25 00:58:32 EST 2016

NAME

allocated for Indranil GhoshNumber of 2 X 2 matrices having all elements in {-n,..,0,..,n} with determinant = permanent.

DATA

1, 45, 225, 637, 1377, 2541, 4225, 6525, 9537, 13357, 18081, 23805, 30625, 38637, 47937, 58621, 70785, 84525, 99937, 117117, 136161, 157165, 180225, 205437, 232897, 262701, 294945, 329725, 367137, 407277, 450241, 496125

OFFSET

0,2

FORMULA

a(x-1)=16*(x^3)-28*(x^2)+16*x-3.

PROG

def t(n):

s=0

for a in range(-n, n+1):

for b in range(-n, n+1):

for c in range(-n, n+1):

for d in range(-n, n+1):

if (a*d-b*c)==(a*d+b*c):

s+=1

return s

for i in range(0, 201):

print str(i)+" "+str(t(i))

CROSSREFS

Cf. A210000.

KEYWORD

allocated

nonn

AUTHOR

Indranil Ghosh, Dec 25 2016

STATUS

approved

editing