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%I #22 Jan 15 2024 12:02:18
%S 1,1,1,2,1,1,3,2,1,1,5,4,2,1,1,9,7,4,2,1,1,16,12,7,4,2,1,1,28,22,13,7,
%T 4,2,1,1,50,39,24,13,7,4,2,1,1,89,70,42,24,13,7,4,2,1,1,159,126,76,43,
%U 24,13,7,4,2,1,1,285,225,137,78,43,24,13,7,4,2,1,1,510
%N Triangle of partitions v(d,c) defined in A002572.
%C Rows are the columns in the table at the end of the Minc reference, read top to bottom. - _Joerg Arndt_, Jan 15 2024
%H Shimon Even and Abraham Lempel, <a href="http://dx.doi.org/10.1016/S0019-9958(72)90149-0">Generation and enumeration of all solutions of the characteristic sum condition</a>, Information and Control 21 (1972), 476-482.
%H H. Minc, <a href="https://doi.org/10.1017/S0013091500021945">A problem in partitions: Enumeration of elements of a given degree in the free commutative entropic cyclic groupoid</a>, Proc. Edinburgh Math. Soc. (2) 11 1958/1959 223-224.
%e Triangle begins
%e 1,
%e 1, 1,
%e 2, 1, 1,
%e 3, 2, 1, 1,
%e 5, 4, 2, 1, 1,
%e 9, 7, 4, 2, 1, 1,
%e 16, 12, 7, 4, 2, 1, 1,
%e 28, 22, 13, 7, 4, 2, 1, 1,
%e 50, 39, 24, 13, 7, 4, 2, 1, 1,
%e 89, 70, 42, 24, 13, 7, 4, 2, 1, 1,
%e 159, 126, 76, 43, 24, 13, 7, 4, 2, 1, 1,
%e 285, 225, 137, 78, 43, 24, 13, 7, 4, 2, 1, 1,
%e ...
%e Rows read backward approach A002843. - _Joerg Arndt_, Jan 15 2024
%p v := proc(c,d) option remember; local i; if d < 0 or c < 0 then 0 elif d = c then 1 else add(v(i,d-c),i=1..2*c); fi; end;
%t v[c_, d_] := v[c, d] = If[d < 0 || c < 0, 0, If[d == c, 1, Sum[v[i, d - c], {i, 1, 2*c}]]]; Table[v[d, c], {c, 1, 13}, {d, 1, c}] // Flatten (* _Jean-François Alcover_, Dec 10 2012, after Maple *)
%Y Cf. A002572, A002573, A002574, A049284, A049285.
%Y See A047913 for another version.
%K nonn,tabl,nice,easy
%O 1,4
%A _N. J. A. Sloane_, _Michael Somos_
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