The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A141388 Cubic form (k=3) of the generalized neo-combinations: t(n,m,k)=(n - m)^k*(m + 1)^k - 2^(n - 1). 0
 0, 6, 6, 23, 60, 23, 56, 208, 208, 56, 109, 496, 713, 496, 109, 184, 968, 1696, 1696, 968, 184, 279, 1664, 3311, 4032, 3311, 1664, 279, 384, 2616, 5704, 7872, 7872, 5704, 2616, 384, 473, 3840, 9005, 13568, 15369, 13568, 9005, 3840, 473, 488, 5320, 13312, 21440 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums are: {0, 12, 106, 528, 1923, 5696, 14540, 33152, 69141, 134096}; Note that the domain here is: {m, 0, n - 1}], {n, 1, 10} and not: {m, 0, n }], {n, 0, 10} The 2^(n-1) term was added to make the result generally symmetrical on the Dynkin / A_n weight domain.. Triangular coefficient sequences of the general form: t(n,m,k)=Floor[((n - m)^k*(m + 1)^k - 2^(n - 1))/n^k); have a Pascal triangle / binomial shape. REFERENCES R. N. Cahn, Semi-Simple Lie Algebras and Their Representations, Dover, NY, 2006, ISBN 0-486-44999-8, p. 139. LINKS FORMULA k=3; t(n,m,k)=(n - m)^k*(m + 1)^k - 2^(n - 1). EXAMPLE {0}, {6, 6}, {23, 60, 23}, {56, 208, 208, 56}, {109, 496, 713, 496, 109}, {184, 968, 1696, 1696, 968, 184}, {279, 1664, 3311, 4032, 3311, 1664, 279}, {384, 2616, 5704, 7872, 7872, 5704, 2616, 384}, {473, 3840, 9005, 13568, 15369, 13568, 9005, 3840, 473}, {488, 5320, 13312, 21440, 26488, 26488, 21440, 13312, 5320, 488} MATHEMATICA 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] CROSSREFS Cf. A003991. Sequence in context: A325998 A322216 A053168 * A255473 A255295 A255475 Adjacent sequences:  A141385 A141386 A141387 * A141389 A141390 A141391 KEYWORD nonn,uned,tabl AUTHOR Roger L. Bagula, Aug 03 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 25 20:01 EDT 2020. Contains 337344 sequences. (Running on oeis4.)