Search: id:A141388
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%I A141388
%S A141388 0,6,6,23,60,23,56,208,208,56,109,496,713,496,109,184,968,1696,1696,968,
%T A141388 184,279,1664,3311,4032,3311,1664,279,384,2616,5704,7872,7872,5704,2616,
%U A141388 384,473,3840,9005,13568,15369,13568,9005,3840,473,488,5320,13312,21440
%N A141388 Cubic form (k=3) of the generalized neo-combinations: t(n,m,k)=(n - m)^k*(m 
               + 1)^k - 2^(n - 1).
%C A141388 Row sums are:
%C A141388 {0, 12, 106, 528, 1923, 5696, 14540, 33152, 69141, 134096};
%C A141388 Note that the domain here is:
%C A141388 {m, 0, n - 1}], {n, 1, 10}
%C A141388 and not:
%C A141388 {m, 0, n }], {n, 0, 10}
%C A141388 The 2^(n-1) term was added to make the result generally symmetrical
%C A141388 on the Dynkin / A_n weight domain..
%C A141388 Triangular coefficient sequences of the general form:
%C A141388 t(n,m,k)=Floor[((n - m)^k*(m + 1)^k - 2^(n - 1))/n^k);
%C A141388 have a Pascal triangle / binomial shape.
%D A141388 R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, 
               NY, 2006, ISBN 0-486-44999-8, p. 139.
%F A141388 k=3; t(n,m,k)=(n - m)^k*(m + 1)^k - 2^(n - 1).
%e A141388 {0},
%e A141388 {6, 6},
%e A141388 {23, 60, 23},
%e A141388 {56, 208, 208, 56},
%e A141388 {109, 496, 713, 496, 109},
%e A141388 {184, 968, 1696, 1696, 968, 184},
%e A141388 {279, 1664, 3311, 4032, 3311, 1664, 279},
%e A141388 {384, 2616, 5704, 7872, 7872, 5704, 2616, 384},
%e A141388 {473, 3840, 9005, 13568, 15369, 13568, 9005, 3840, 473},
%e A141388 {488, 5320, 13312, 21440, 26488, 26488, 21440, 13312, 5320, 488}
%t A141388 Clear[T, n, m, a]; T[n_, m_] = (n - m)^3*(m + 1)^3 - 2^(n - 1); a = Table[Table[T[n, 
               m], {m, 0, n - 1}], {n, 1, 10}]; Flatten[a]
%Y A141388 Cf. A003991.
%Y A141388 Sequence in context: A004983 A034695 A053168 this_sequence A087236 A077193 
               A056482
%Y A141388 Adjacent sequences: A141385 A141386 A141387 this_sequence A141389 A141390 
               A141391
%K A141388 nonn,uned,tabl
%O A141388 1,2
%A A141388 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Aug 03 2008

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