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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A096466 Triangle T(n,k), read by rows, formed by setting all entries in the zeroth column ((n,0) entries) and the main diagonal ((n,n) entries) to powers of 2 with all other entries formed by the recursion T(n,k) = T(n-1,k) + T(n,k-1). 0
1, 2, 2, 4, 6, 4, 8, 14, 18, 8, 16, 30, 48, 56, 16, 32, 62, 110, 166, 182, 32, 64, 126, 236, 402, 584, 616, 64, 128, 254, 490, 892, 1476, 2092, 2156, 128, 256, 510, 1000, 1892, 3368, 5460, 7616, 7744, 256, 512, 1022, 2022, 3914, 7282, 12742, 20358, 28102, 28358, 512 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

T(n,k) = T(n-1,k) + T(n,k-1) for n >= 2 and 1 <= k <= n - 1 with T(n,0) = T(n,n) = 2^n for n >= 0.

The n-th row sum equals A082590(n), which is the expansion of 1/(1 - 2*x)/sqrt(1 - 4*x) and equals 2^n * JacobiP(n, 1/2, -1-n, 3).

First column is T(n,1) = A000918(n+1) = 2^(n+1) - 2.

From Petros Hadjicostas, Aug 06 2020: (Start)

T(n,2) = 2^(n+2) - 2*n - 8 for n >= 2.

T(n+1,n) = 2^n + Sum_{k=0..n} T(n,k) = 2^n + A082590(n).

Bivariate o.g.f.: ((1 - x)*(1 - y)/(1 - 2*x) - x*y/sqrt(1 - 4*x*y))/((1 - 2*x*y)*(1 - x - y)). (End)

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

From Petros Hadjicostas, Aug 06 2020: (Start)

Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:

   1;

   2,   2;

   4,   6,   4;

   8,  14,  18,   8;

  16,  30,  48,  56,  16;

  32,  62, 110, 166, 182,  32;

  64, 126, 236, 402, 584, 616, 64;

  ... (End)

PROG

(PARI) T(n, k) = if ((k==0) || (n==k), 2^n, if ((n<0) || (k<0), 0, if (n>k, T(n-1, k) + T(n, k-1), 0)));

for(n=0, 10, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Aug 07 2020

CROSSREFS

Cf. A000918, A082590.

Sequence in context: A318343 A318024 A320409 * A088965 A059474 A252828

Adjacent sequences:  A096463 A096464 A096465 * A096467 A096468 A096469

KEYWORD

nonn,tabl

AUTHOR

Gerald McGarvey, Aug 12 2004

EXTENSIONS

Offset changed to 0 by Petros Hadjicostas, Aug 06 2020

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 November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)