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!)
A120871 a(n) is the value of j for row n of the fixed-j dispersion for Q = 8. 1
1, 4, 2, 7, 8, 17, 7, 18, 17, 32, 14, 31, 9, 28, 23, 46, 16, 41, 34, 63, 25, 56, 14, 47, 36, 73, 23, 62, 49, 92, 34, 79, 64, 113, 47, 98, 28, 81, 62, 119, 41, 100, 79, 142, 56, 121, 31, 98, 73, 144, 46, 119, 92, 169, 63, 142, 113, 196, 82, 167, 49, 136, 103, 194 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence results from A087056 by deleting duplicates.

LINKS

Table of n, a(n) for n=1..64.

Clark Kimberling, The equation (j+k+1)^2 - 4*k = Q*n^2 and related dispersions, Journal of Integer Sequences, 10 (2007), Article #07.2.7.

EXAMPLE

For each positive integer n, there is a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 8*n^2. This representation is used to define the fixed-j dispersion for Q = 8, given by A120860, having northwest corner:

  1,  5,  29, 169, ...

  2, 10,  58, 338, ...

  3, 17,  99, 577, ...

  4, 22, 128, 746, ...

  ...

The pair (j,k) for each n, shown in the position occupied by n in the above array, is shown here:

  (1,2), (1,14),  (1,82),  (1,478), ...

  (4,1), (4,25), (4,161),  (4,953), ...

  (2,7), (2,47), (2,279), (2,1631), ...

  (7,4), (7,56), (7,356), (7,2104), ...

  ...

The fixed-j for row 1 is a(1) = 1;

the fixed-j for row 2 is a(2) = 4; etc.

(For example, (4 + 25 + 1)^2 - 4*25 = 8*10^2.)

PROG

(PARI) f(n) = 3*n + 2*sqrtint(2*n^2); \\ A098021

unused(listus) = {my(v=vecsort(Vec(listus))); for (i=1, vecmax(v), if (!vecsearch(v, i), return (i)); ); };

D(nb) = {my(m = matrix(nb, nb), t); my(listus = List); for (g=1, nb, if (g==1, t = 1, t = unused(listus)); m[g, 1]=t; listput(listus, t); t = f(t); m[g, 2]=t; listput(listus, t); for (h=3, nb, t = 6*m[g, h-1] - m[g, h-2]; m[g, h] = t; listput(listus, t); ); ); m; }; \\ A120860

q(n) = 2*n^2 - sqrtint(2*n^2)^2; \\ A087056

lista(nn) = my(m=D(nn)); vector(nn, n, q(m[n, 1])); \\ Michel Marcus, Jul 09 2020

CROSSREFS

Cf. A087056, A098021, A120860.

Sequence in context: A128226 A049817 A203575 * A019689 A332651 A072009

Adjacent sequences:  A120868 A120869 A120870 * A120872 A120873 A120874

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 10 2006

EXTENSIONS

More terms from Michel Marcus, Jul 09 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 April 10 22:19 EDT 2021. Contains 342856 sequences. (Running on oeis4.)