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A013574 Minimal scope of an (n,2) difference triangle. 3
3, 7, 10, 12, 15, 19, 22, 24, 27, 31, 34, 36, 39, 43, 46, 48, 51, 55, 58, 60, 63, 67, 70, 72, 75, 79, 82, 84, 87, 91, 94, 96, 99, 103, 106, 108, 111, 115, 118, 120, 123, 127, 130, 132, 135, 139, 142, 144, 147, 151, 154, 156, 159, 163, 166, 168, 171, 175, 178, 180, 183, 187, 190 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

A row or column of array in A234943.

A319279 is an essentially identical sequence.

Sequence in context: A225552 A147683 A319279 * A235915 A310178 A310179

Adjacent sequences:  A013571 A013572 A013573 * A013575 A013576 A013577

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)