A378248 Number of sets of chess pieces whose collective material value adds to n.
1, 1, 1, 3, 3, 4, 7, 7, 9, 14, 15, 18, 25, 27, 32, 42, 45, 52, 66, 71, 81, 99, 106, 120, 143, 153, 171, 200, 214, 237, 273, 291, 320, 364, 387, 423, 476, 505, 549, 612, 648, 701, 775, 819, 882, 969, 1022, 1096, 1197, 1260, 1347, 1463, 1537, 1638, 1771, 1858
Offset: 0
Examples
For n=4, the a(4)=3 sets of pieces are {1, 1, 1, 1}, {3a, 1}, {3b, 1}, where the knight and bishop both worth 3 are labeled 3a and 3b.
For n=9 the a(9)=14 solutions are {1, 1, 1, 1, 1, 1, 1, 1, 1}, {3a, 1, 1, 1, 1, 1, 1}, {3b, 1, 1, 1, 1, 1, 1}, {3a, 3a, 1, 1, 1}, {3a, 3b, 1, 1, 1}, {3b, 3b, 1, 1, 1}, {3a, 3a, 3a}, {3a, 3a, 3b}, {3a, 3b, 3b}, {3b, 3b, 3b}, {5, 1, 1, 1, 1}, {5, 3a, 1}, {5, 3b, 1}, and {9}.
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,1,-2,1,-2,3,-1,1,-3,2,-1,2,-1,2,-2,0,-1,1).
Crossrefs
Cf. A029041.
Formula
G.f.: 1/((1-x)*(1-x^3)^2*(1-x^5)*(1-x^9)). - Andrew Howroyd, Nov 20 2024
Comments