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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A133819 Triangle whose rows are sequences of increasing squares: 1; 1,4; 1,4,9; ... . 14
1, 1, 4, 1, 4, 9, 1, 4, 9, 16, 1, 4, 9, 16, 25, 1, 4, 9, 16, 25, 36, 1, 4, 9, 16, 25, 36, 49, 1, 4, 9, 16, 25, 36, 49, 64, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Reading the triangle by rows produces the sequence 1,1,4,1,4,9,1,4,9,16,..., analogous to A002260.

Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. A133819 is reluctant sequence of A000290. - Boris Putievskiy, Jan 11 2013

LINKS

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened

M. de Frenicle, Methode pour trouver la solutions des problemes par les exclusions, in: Divers ouvrages de mathematiques et de physique par messieurs de l'academie royale des sciences, (1693) pp 1-44, page 11. - Paul Curtz, Aug 18 2008

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO].

FORMULA

T(n, k) = k^2, n >= k >= 1.

O.g.f.: (1+qx)/((1-x)(1-qx)^3) = 1 + x(1 + 4q) + x^2(1 + 4q + 9q^2) + ... .

a(n) = A000290(m+1), where m = n-t(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Jan 11 2013

EXAMPLE

The triangle T(n, k) starts:

1;

1, 4;

1, 4, 9;

1, 4, 9, 16;

1, 4, 9, 16, 25;

MATHEMATICA

With[{sqs=Range[12]^2}, Flatten[Table[Take[sqs, n], {n, 12}]]] (* Harvey P. Dale, Sep 09 2012 *)

PROG

(Haskell)

a133819 n k = a133819_tabl !! (n-1) !! (k-1)

a133819_row n = a133819_tabl !! (n-1)

a133819_tabl = map (`take` (tail a000290_list)) [1..]

-- Reinhard Zumkeller, Nov 11 2012

CROSSREFS

Cf. A215630, A215631, A000290, A002260.

Cf. A048152, A060036.

Sequence in context: A131112 A141225 A079185 * A274092 A021245 A007891

Adjacent sequences:  A133816 A133817 A133818 * A133820 A133821 A133822

KEYWORD

easy,nonn,tabl

AUTHOR

Peter Bala, Sep 25 2007

EXTENSIONS

Offset changed by Reinhard Zumkeller, Nov 11 2012

T(n, k) formula added by Wolfdieter Lang, Dec 02 2014

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 22 00:25 EDT 2017. Contains 292326 sequences.