cp's OEIS Frontend

A378248 Number of sets of chess pieces whose collective material value adds to n.

%I A378248 #12 Dec 06 2024 11:19:51
%S A378248 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,
%T A378248 153,171,200,214,237,273,291,320,364,387,423,476,505,549,612,648,701,
%U A378248 775,819,882,969,1022,1096,1197,1260,1347,1463,1537,1638,1771,1858
%N A378248 Number of sets of chess pieces whose collective material value adds to n.
%C A378248 The pieces are valued pawn=1, knight=3, bishop=3, rook=5,  queen=9.
%C A378248 The knight and bishop are different ways to add 3 into the total.
%C A378248 So a(n) is the number of ways to partition n into a sum of parts 1, 3, 5, 9 with two types of 3.
%H A378248 <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,1,-2,1,-2,3,-1,1,-3,2,-1,2,-1,2,-2,0,-1,1).
%F A378248 G.f.: 1/((1-x)*(1-x^3)^2*(1-x^5)*(1-x^9)). - _Andrew Howroyd_, Nov 20 2024
%e A378248 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.
%e A378248 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}.
%Y A378248 Cf. A029041.
%K A378248 nonn,easy
%O A378248 0,4
%A A378248 _David W. Ziegler_, Nov 20 2024