A006185 Number of pair-coverings with largest block size 3. (Formerly M3266)

1, 4, 6, 7, 7, 12, 12, 19, 21, 26, 26, 35, 35, 46, 48, 57, 57, 70, 70, 85, 87, 100, 100, 117, 117, 136, 138, 155, 155, 176, 176, 199, 201, 222, 222, 247, 247, 274, 276, 301, 301, 330, 330, 361, 363, 392, 392, 425, 425, 460, 462, 495, 495, 532

Offset

3,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. G. Stanton, J. L. Allston and D. D. Cowan, Pair-coverings with restricted largest block length, Ars Combin., 11 (1981), 85-98.

M. J. Grannell, T. S. Griggs, K. A. S. Quinn, R. G. Stanton, A census of minimum pair-coverings with restricted largest block length, Ars Combin., 52 (1999).

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..5000

R. G. Stanton, J. L. Allston and D. D. Cowan, Pair-coverings with restricted largest block length, Ars Combin., 11 (1981), 85-98. (Annotated scanned copy)

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

Formula

a(n) = n*(n-1)/6 if n == 1 or 3 (mod 6), a(n) = n*(n+1)/6 if n == 0 or 2 (mod 6), a(n) = (n^2+n+4)/6 if n == 4 (mod 6), and a(n) = (n^2-n+16)/6 if n == 5 (mod 6). [From Grannell et al.] - Sean A. Irvine, Jan 17 2017

G.f.: -x^3*(1 + 3*x + x^2 - 2*x^3 + 4*x^5 - x^7 - 2*x^4 - x^6 + x^8) / ( (x^2-x+1)*(1+x+x^2)*(1+x)^2*(x-1)^3 ). - R. J. Mathar, Jan 26 2017

Mathematica

LinearRecurrence[{1, 1, -1, 0, 0, 1, -1, -1, 1}, {1, 4, 6, 7, 7, 12, 12, 19, 21}, 100] (* Vincenzo Librandi, Jan 27 2017 *)

Prog

(Magma) I:=[1, 4, 6, 7, 7, 12, 12, 19, 21]; [n le 9 select I[n] else Self(n-1)+Self(n-2)-Self(n-3)+Self(n-6)-Self(n-7)-Self(n-8)+Self(n-9): n in [1..60]]; // Vincenzo Librandi, Jan 27 2017

Crossrefs

Sequence in context: A266148 A011275 A205684 * A169788 A369802 A300707

Adjacent sequences: A006182 A006183 A006184 * A006186 A006187 A006188

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved