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

Author

David S. Newman, Dec 10 2005

Keywords

• nonn
• easy

Examples

			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.
		

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).

Crossrefs

Cf. A008724.

Programs

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

Mathematica

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

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

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

Extensions

More terms from Jon E. Schoenfield, Dec 20 2013