A112422 Number of 6-element subsets of {1,2,3,...,n} for which the sum-set has 13 elements.

3, 11, 19, 27, 35, 43, 54, 65, 81, 97, 113, 129, 148, 167, 186, 210, 234, 258, 285, 312, 339, 366, 398, 430, 465, 500, 535, 570, 605, 645, 688, 731, 774, 817, 860, 903, 954, 1005, 1056, 1107, 1158, 1209, 1263, 1322, 1381, 1440, 1499, 1558, 1620, 1682, 1749

Offset

7,1

Links

Colin Barker, Table of n, a(n) for n = 7..1000

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

Formula

G.f.: x^7*(3 +8*x +8*x^2 +8*x^3 +8*x^4 +8*x^5 +8*x^6) / ((1 -x)^3*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)). - Corrected by Colin Barker, Jan 10 2017

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 1}, {3, 11, 19, 27, 35, 43, 54, 65, 81, 97, 113, 129, 148, 167}, 60] (* Harvey P. Dale, Jul 01 2020 *)

Prog

(PARI) Vec(x^7*(3 +8*x +8*x^2 +8*x^3 +8*x^4 +8*x^5 +8*x^6) / ((1 -x)^3*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6)) + O(x^60)) \\ Colin Barker, Jan 10 2017

Crossrefs

Sequence in context: A043433 A078583 A017101 * A289840 A125994 A137295

Adjacent sequences: A112419 A112420 A112421 * A112423 A112424 A112425

Keyword

nonn,easy

Author

David S. Newman, Dec 10 2005

Extensions

Edited by Colin Barker, Jan 10 2017

Status

approved