login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A204533 Triangle T(n,k), read by rows, given by (0, 1, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 2
1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 8, 7, 3, 1, 0, 21, 22, 12, 4, 1, 0, 55, 67, 43, 18, 5, 1, 0, 144, 200, 147, 72, 25, 6, 1, 0, 377, 588, 486, 271, 110, 33, 7, 1, 0, 987, 1708, 1566, 976, 450, 158, 42, 8, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Riordan array (1, x*(1-x)^2/(1-3*x+x^2)).

Antidiagonal sums: see A052946.

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150).

FORMULA

Sum_{k=0..n} T(n,k) = A204200(n+1).

T(n,k) = 3*T(n-1,k) + T(n-1,k-1) + T(n-3,k-1) - T(n-2,k) - 2*T(n-2,k-1).

G.f.: (-1 + 3*x - x^2)/(-1 + 3*x - x^2 + x*y - 2*x^2*y + x^3*y). - R. J. Mathar, Aug 11 2015

T(n,m) = Sum_{k=0..n-1} C(k,m-1)*C(n-2*m+k,n-k-1), T(0,0)=1. - Vladimir Kruchinin, Sep 27 2018

EXAMPLE

Triangle begins:

  1;

  0,   1;

  0,   1,   1;

  0,   3,   2,   1;

  0,   8,   7,   3,  1;

  0,  21,  22,  12,  4,  1;

  0,  55,  67,  43, 18,  5, 1;

  0, 144, 200, 147, 72, 25, 6, 1;

MATHEMATICA

Table[Sum[Binomial[k, m - 1] Binomial[n - 2 m + k, n - k - 1], {k, 0, n - 1}] + Boole[n == m == 0], {n, 0, 9}, {m, 0, n}] // Flatten (* Michael De Vlieger, Sep 26 2018 *)

PROG

(Maxima)

T(n, m):= if n=0 and m=0 then 1 else sum(binomial(k, m-1)*binomial(n-2*m+k, n-k-1), k, 0, n-1); /* Vladimir Kruchinin, Sep 27 2018 */

(PARI) T(n, k) = if ((n==0) && (k==0), 1, sum(i=0, n-1, binomial(i, k-1)*binomial(n-2*k+i, n-i-1))); \\ Michel Marcus, Sep 27 2018

CROSSREFS

Cf. diagonals: A000007, A088305, A000012, A001477, A055998.

Sequence in context: A111460 A035327 A004444 * A259790 A246654 A325111

Adjacent sequences:  A204530 A204531 A204532 * A204534 A204535 A204536

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jan 16 2012

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 05:22 EDT 2019. Contains 328146 sequences. (Running on oeis4.)