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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A265159 Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = 5 + 9*A005836(2^(k - 1)*(2 n - 1)), n,k >= 1. 2
5, 32, 14, 86, 95, 41, 113, 257, 284, 122, 248, 338, 770, 851, 365, 275, 743, 1013, 2309, 2552, 1094, 329, 824, 2228, 3038, 6926, 7655, 3281, 356, 986, 2471, 6683, 9113, 20777, 22964, 9842, 734, 1067, 2957, 7412, 20048, 27338, 62330, 68891, 29525 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture 1: The array contains without duplication all possible "block numbers" defined in A265100.

LINKS

Table of n, a(n) for n=1..45.

FORMULA

Conjecture 2: A(n,k) = (A055246(n)*3^k + 1)/2, so the array and A265100 are related to Cantor's ternary set.

G.f. for row n (conjectured): f(n,x) = x*(A265100(n)-(A265100(n)+1)*x)/((1-x)*(1-3*x)).

EXAMPLE

Array A begins:

.      5    14    41    122    365    1094    3281     9842    29525

.     32    95   284    851   2552    7655   22964    68891   206672

.     86   257   770   2309   6926   20777   62330   186989   560966

.    113   338  1013   3038   9113   27338   82013   246038   738113

.    248   743  2228   6683  20048   60143  180428   541283  1623848

.    275   824  2471   7412  22235   66704  200111   600332  1800995

.    329   986  2957   8870  26609   79826  239477   718430  2155289

.    356  1067  3200   9599  28796   86387  259160   777479  2332436

.    734  2201  6602  19805  59414  178241  534722  1604165  4812494

MATHEMATICA

(* Array: *)

a005836[1] := 0; a005836[n_] := If[OddQ[n], 3*a005836[Floor[(n + 1)/2]], a005836[n - 1] + 1]; a265159[n_, k_] := 5 + 9*a005836[2^(k - 1)*(2 n - 1)]; Grid[Table[a265159[n, k], {n, 9}, {k, 9}]]

(* Array antidiagonals flattened: *)

a005836[1] := 0; a005836[n_] := If[OddQ[n], 3*a005836[Floor[(n + 1)/2]], a005836[n - 1] + 1]; a265159[n_, k_] := 5 + 9*a005836[2^(k - 1)*(2 n - 1)]; Flatten[Table[a265159[n - k + 1, k], {n, 9}, {k, n}]]

CROSSREFS

Cf. A005836, A055246, A265100, A265104, A265161.

Sequence in context: A062631 A156027 A100840 * A247549 A140154 A073694

Adjacent sequences:  A265156 A265157 A265158 * A265160 A265161 A265162

KEYWORD

nonn,tabl

AUTHOR

L. Edson Jeffery, Dec 03 2015

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 15 11:14 EST 2019. Contains 329144 sequences. (Running on oeis4.)