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!)
A087322 Triangle T read by rows: T(n, 1) = 2*n + 1. For 1 < k <= n, T(n, k) = 2*T(n,k-1) + 1. 3
3, 5, 11, 7, 15, 31, 9, 19, 39, 79, 11, 23, 47, 95, 191, 13, 27, 55, 111, 223, 447, 15, 31, 63, 127, 255, 511, 1023, 17, 35, 71, 143, 287, 575, 1151, 2303, 19, 39, 79, 159, 319, 639, 1279, 2559, 5119, 21, 43, 87, 175, 351, 703, 1407, 2815, 5631, 11263, 23, 47, 95 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

With T(n,0) = n for n >= 0, this becomes J. M. Bergot's triangular array in the definition of A190730. - Petros Hadjicostas, Feb 15 2021

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

From Petros Hadjicostas, Feb 15 2021: (Start)

Sum_{k=1..n} T(n,k) = A190730(n).

T(n,2) = 4*n + 3 for n >= 2.

T(n,n) = A087323(n).

T(n,n-1) = A099035(n) = (n+1)*2^(n-1) - 1 for n >= 2.

Recurrence: T(n,k) = 3*T(n,k-1) - 2*T(n,k-2) for n >= 2 and 2 <= k <= n with initial conditions the values of T(n, 1) and T(n,2).

Bivariate o.g.f.: Sum_{n,k>=1} T(n,k)*x^n*y^k = (4*x^3*y^2 - 2*x^2*y - 4*x*y - x + 3)*x*y/((1 - 2*x*y)^2*(1 - x*y)*(1 - x)^2). (End)

EXAMPLE

Triangle T(n,k) (with rows n >= 1 and columns k = 1..n) begins:

   3;

   5, 11;

   7, 15, 31;

   9, 19, 39,  79;

  11, 23, 47,  95, 191;

  13, 27, 55, 111, 223, 447;

  15, 31, 63, 127, 255, 511, 1023;

  17, 35, 71, 143, 287, 575, 1151, 2303;

  19, 39, 79, 159, 319, 639, 1279, 2559, 5119;

  ...

CROSSREFS

Cf. A087323, A099035, A190730.

Sequence in context: A073653 A225487 A145398 * A094747 A300783 A287939

Adjacent sequences:  A087319 A087320 A087321 * A087323 A087324 A087325

KEYWORD

nonn,tabl,easy

AUTHOR

Amarnath Murthy, Sep 03 2003

EXTENSIONS

Edited and extended by David Wasserman, May 06 2005

Name edited by Petros Hadjicostas, Feb 15 2021

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 June 13 06:07 EDT 2021. Contains 344981 sequences. (Running on oeis4.)