The On-Line Encyclopedia of Integer Sequences (OEIS)

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A212578

Number of (w,x,y,z) with all terms in {1,...,n} and |w-x| = 2*|x-y| - |y-z|.
(history; published version)

#17 by Charles R Greathouse IV at Thu Sep 08 08:46:02 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 45); [0] cat Coefficients(R!( x*(1+2*x +4*x^2+2*x^3+x^4)/(1-2*x-x^2+4*x^3-x^4-2*x^5+x^6) )); // G. C. Greubel, Apr 10 2019

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#16 by Michel Marcus at Thu Apr 11 09:23:43 EDT 2019

STATUS

reviewed

approved

#15 by Joerg Arndt at Thu Apr 11 09:11:54 EDT 2019

STATUS

proposed

reviewed

#14 by G. C. Greubel at Wed Apr 10 21:20:32 EDT 2019

STATUS

editing

proposed

#13 by G. C. Greubel at Wed Apr 10 21:19:32 EDT 2019

NAME

Number of (w,x,y,z) with all terms in {1,...,n} and |w-x| = 2*|x-y| - |y-z|.

LINKS

G. C. Greubel, <a href="/A212578/b212578.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6).

G.f.: (x *(1 + 2*x^2 + 4*x^3 2 + 2*x^4 3 + x^54)/(1 - 2*x - x^2 + 4*x^3 - x^4 - 2*x^5 + x^6).

PROG

(PARI) my(x='x+O('x^45)); concat([0], Vec(x*(1+2*x+4*x^2+2*x^3+x^4)/(1 -2*x-x^2+4*x^3 -x^4-2*x^5+x^6))) \\ G. C. Greubel, Apr 10 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 45); [0] cat Coefficients(R!( x*(1+2*x +4*x^2+2*x^3+x^4)/(1-2*x-x^2+4*x^3-x^4-2*x^5+x^6) )); // G. C. Greubel, Apr 10 2019

(Sage) (x*(1+2*x+4*x^2+2*x^3+x^4)/(1-2*x-x^2+4*x^3-x^4-2*x^5+x^6) ).series(x, 45).coefficients(x, sparse=False) # G. C. Greubel, Apr 10 2019

STATUS

proposed

editing

#12 by Georg Fischer at Wed Apr 10 12:55:26 EDT 2019

STATUS

editing

proposed

#11 by Georg Fischer at Wed Apr 10 12:55:10 EDT 2019

LINKS

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 1, -4, 1, 2, -1).

MATHEMATICA

LinearRecurrence[{1, 2, 1, -4, 1, 2, -1}, {0, 1, 4, 13, 28, 55, 92}, 45] (* signature corrected by _Georg Fischer_, Apr 10 2019 *)

STATUS

approved

editing

Discussion

Wed Apr 10

12:55

Georg Fischer: Found by joeis testing.

#10 by Ray Chandler at Sat Aug 01 10:22:09 EDT 2015

STATUS

editing

approved

#9 by Ray Chandler at Sat Aug 01 10:22:06 EDT 2015

LINKS

<a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, -4, 1, 2, -1).

STATUS

approved

editing

#8 by Bruno Berselli at Fri Jun 08 14:56:11 EDT 2012

STATUS

editing

approved