A392899 Number of bipartite complete simple games with a maximum number of minimal winning pairs.

0, 1, 1, 6, 2, 12, 3, 19, 4, 27, 5, 36, 6, 46, 7, 57, 8, 69, 9, 82, 10, 96, 11, 111, 12, 127, 13, 144, 14, 162, 15, 181, 16, 201, 17, 222, 18, 244, 19, 267, 20, 291, 21, 316, 22, 342, 23, 369, 24, 397, 25, 426, 26, 456, 27, 487, 28, 519, 29, 552, 30, 586, 31

Offset

1,4

Links

Table of n, a(n) for n=1..63.

Josep Freixas and Dani Samaniego, On the enumeration of bipartite simple games, Discrete Applied Mathematics, 297 (2021), 129-141.

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

a(n) = (1/8)*(n^2+14n-24) if n is even.

a(n) = (1/2)*(n-1) if n is odd.

G.f.: (x^5+6*x^4-x^3-10*x^2+3)/((x-1)^3*(x+1)^3).

Mathematica

LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 1, 6, 2, 12}, 70] (* Amiram Eldar, Feb 24 2026 *)

Crossrefs

Bisections give: A001477, A051936 (shifted).

Sequence in context: A392144 A040035 A065272 * A070394 A065174 A065284

Adjacent sequences: A392896 A392897 A392898 * A392900 A392901 A392902

Keyword

nonn,easy

Author

Josep Freixas, Feb 24 2026

Status

approved