A228949 Coins left when packing boomerangs into n X n coins.

4, 3, 7, 13, 6, 13, 22, 9, 19, 31, 12, 25, 40, 15, 31, 49, 18, 37, 58, 21, 43, 67, 24, 49, 76, 27, 55, 85, 30, 61, 94, 33, 67, 103, 36, 73, 112, 39, 79, 121, 42, 85, 130, 45, 91, 139, 48, 97, 148, 51, 103, 157, 54, 109, 166, 57

Offset

2,1

Comments

The coins left after packing boomerangs into n X n coins using the same rule as A229593. See illustration in links.

Links

Table of n, a(n) for n=2..57.

Kival Ngaokrajang, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Formula

G.f. -x^2*(-4-3*x-7*x^2-5*x^3+x^5) / ( (x-1)^2*(1+x+x^2)^2 ). - R. J. Mathar, Oct 16 2013

Mathematica

LinearRecurrence[{0, 0, 2, 0, 0, -1}, {4, 3, 7, 13, 6, 13}, 80] (* Harvey P. Dale, Jan 19 2019 *)

Prog

(Small Basic)
u[2]=4
d[3]=-1
d[4]=4
d[5]=6
For n=2 To 100
  If n+1 >=6 Then
    If Math.Remainder(n+1, 3)=0 Then
      d[n+1]=d[n-2]-6
    Else
      d[n+1]=d[n-2]+3
    EndIf
  EndIf
  u[n+1]=u[n]+d[n+1]
  TextWindow.Write(u[n]+", ")
EndFor

Crossrefs

Cf. A229593 (Boomerangs), A229598 (Voids), A017209 (trisection), A008585 (trisection), A016921 (trisection).

Sequence in context: A244335 A275818 A245300 * A048227 A213661 A176083

Adjacent sequences: A228946 A228947 A228948 * A228950 A228951 A228952

Keyword

nonn,easy

Author

Kival Ngaokrajang, Oct 05 2013

Status

approved