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!)
 A103451 Triangular array T read by rows: T(n, 0) = T(n, n) = 1, T(n, k) = 0 for 0 <= k <= n. 32
 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Equals Pascal's triangle (A007318) where all elements > 1 are replaced with zero. Therefore it might be called "binomial skeleton". Row sums are in A040000, antidiagonal sums are in A040001. When construed as a lower triangular matrix, the matrix inverse is A103452. LINKS Michael De Vlieger, Rows n = 0..140 of triangle, flattened Carl M. Bender and Gerald V. Dunne, Polynomials and operator orderings, J. Math. Phys. 29 (1988), 1727-1731. FORMULA a(n) = A097806(n-1) for n > 0. - Philippe Deléham, Oct 16 2007 T(n,k) = C(n,k-n) + C(n,-k) - C(0,n+k), 0 <= k <= n. - Eric Werley, Jul 01 2011 EXAMPLE First few rows are:   1;   1, 1;   1, 0, 1;   1, 0, 0, 1;   1, 0, 0, 0, 1;   1, 0, 0, 0, 0, 1;   ... MATHEMATICA Table[Boole[n == 0 || Mod[k, n] == 0], {n, 0, 14}, {k, 0, n}] (* or *) Table[Binomial[n, k - n] + Binomial[n, -k] - Binomial[0, n + k], {n, 0, 14}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jul 19 2016 *) PROG (MAGMA) r:=14; T:=ScalarMatrix(r, 1); for n in [1..r] do T[n, 1]:=1; end for; &cat[ [ T[n, k]: k in [1..n] ]: n in [1..r] ]; (MAGMA) /* As triangle */ [[Binomial(n, k-n)+Binomial(n, -k)-Binomial(0, n+k): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jul 20 2016 (PARI) for(n=0, 15, for(k=0, n, print1(if(k==0||k==n, 1, 0), ", "))) \\ G. C. Greubel, Dec 08 2018 (Sage) def A103451(n, k): return 1 if (k==0 or k==n) else 0 flatten([[A103451(n, k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Feb 14 2021 CROSSREFS Cf. A007318, A040000, A040001, A097806, A103452. Sequence in context: A189289 A270885 A127972 * A103452 A131219 A127970 Adjacent sequences:  A103448 A103449 A103450 * A103452 A103453 A103454 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Feb 06 2005 EXTENSIONS Edited by Klaus Brockhaus, Jan 26 2011 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 June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)