A112421 Number of 6 element subsets of {1,2,3,...,n} for which the sum-set has 12 elements.

2, 4, 6, 8, 10, 12, 16, 20, 24, 28, 32, 36, 42, 48, 54, 60, 66, 72, 80, 88, 96, 104, 112, 120, 130, 140, 150, 160, 170, 180, 192, 204, 216, 228, 240, 252, 266, 280, 294, 308, 322, 336, 352, 368, 384, 400, 416, 432, 450, 468, 486, 504, 522, 540, 560, 580, 600

Offset

7,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 7..1000

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

Formula

G.f.: 2*x^7/((1-x)^2*(1-x^6)).

a(n) = 2*A008724(n-3). a(n) = 2*a(n-1) - a(n-2) + a(n-6) - 2*a(n-7) + a(n-8). - R. J. Mathar, Jul 26 2010

a(n) = 2*j*(n-3*j-3), where j=floor(n/6). - Jon E. Schoenfield, Dec 20 2013

Example

a(7)=2 because the two sets {1 2 3 4 5 7} and {1 3 4 5 6 7} have sum-sets
{2 3 4 5 6 7 8 9 10 11 12 14} and {2 4 5 6 7 8 9 10 11 12 13 14}, respectively and each of these sum-sets has 12 elements.

Mathematica

CoefficientList[Series[2/((1 - x)^2 (1 - x^6)), {x, 0, 100}], x] (* Vincenzo Librandi, Dec 21 2013 *)

Prog

(PARI) lista(n) = {my(x = xx + O(xx^n)); gf = 2*x^7/((1-x)^2*(1-x^6)); for (i=7, n-1, print1(polcoeff(gf, i, xx), ", ")); } \\ - Michel Marcus, Dec 20 2013
(Magma) I:=[2, 4, 6, 8, 10, 12, 16, 20]; [n le 8 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-6)-2*Self(n-7)+Self(n-8): n in [1..70]]; // Vincenzo Librandi, Dec 21 2013

Crossrefs

Cf. A008724.

Sequence in context: A331079 A274284 A375473 * A320674 A022483 A100180

Adjacent sequences: A112418 A112419 A112420 * A112422 A112423 A112424

Keyword

nonn,easy

Author

David S. Newman, Dec 10 2005

Extensions

More terms from Jon E. Schoenfield, Dec 20 2013

Status

approved