OFFSET
1,1
COMMENTS
a(n)*Pi is also the total length of irregular spiral (center points: 1, 2, 5, 3, 4) after n-rotations. - Kival Ngaokrajang, Jan 08 2014
REFERENCES
CRC Handbook of Combinatorial Designs, 1996, p. 315.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Y. M. Chee, C. J. Colbourn, Constructions for difference triangle sets, arXiv:0712.2553 [cs.IT], 2007.
Kival Ngaokrajang, Illustration of irregular spiral (center points: 1, 2, 5, 3, 4)
J. B. Shearer, Difference Triangle Sets: Known optimal solutions.
J. B. Shearer, Difference Triangle Sets: Discoverers
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
a(n) = 3n if n = {0,1} (mod 4). a(n) = 3n+1 if n = {2,3} (mod 4). [Chee Theor. 2] - R. J. Mathar, Nov 28 2016
G.f.: x*(3+x+2*x^2) / ( (x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 28 2016
From Colin Barker, Nov 25 2017: (Start)
a(n) = (-1/4 - i/4) * ((-1+i) + (-i)^n - i*i^n - (6-6*i)*n).
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.
(End)
MAPLE
A013574 := proc(n)
if modp(n, 4) in {0, 1} then
3*n ;
else
3*n+1 ;
end if;
end proc: # R. J. Mathar, Nov 28 2016
MATHEMATICA
LinearRecurrence[{2, -2, 2, -1}, {3, 7, 10, 12}, 63] (* Jean-François Alcover, Nov 24 2017 *)
PROG
(PARI) Vec(x*(3 + x + 2*x^2) / ((1 - x)^2*(1 + x^2)) + O(x^40)) \\ Colin Barker, Nov 25 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
