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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286099 Square array read by antidiagonals: A(n,k) = T(n OR k, n AND k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and OR is bitwise-or (A003986). 5
0, 2, 2, 5, 4, 5, 9, 9, 9, 9, 14, 13, 12, 13, 14, 20, 20, 18, 18, 20, 20, 27, 26, 27, 24, 27, 26, 27, 35, 35, 35, 35, 35, 35, 35, 35, 44, 43, 42, 43, 40, 43, 42, 43, 44, 54, 54, 52, 52, 50, 50, 52, 52, 54, 54, 65, 64, 65, 62, 61, 60, 61, 62, 65, 64, 65, 77, 77, 77, 77, 73, 73, 73, 73, 77, 77, 77, 77, 90, 89, 88, 89, 90, 85, 84, 85, 90, 89, 88, 89, 90 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The array is read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10584; the first 145 antidiagonals of array

MathWorld, Pairing Function

FORMULA

A(n,k) = T(A003986(n,k), A004198(n,k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, that is, as a pairing function from [0, 1, 2, 3, ...] x [0, 1, 2, 3, ...] to [0, 1, 2, 3, ...].

EXAMPLE

The top left 0 .. 12 x 0 .. 12 corner of the array:

   0,   2,   5,   9,  14,  20,  27,  35,  44,  54,  65,  77,  90

   2,   4,   9,  13,  20,  26,  35,  43,  54,  64,  77,  89, 104

   5,   9,  12,  18,  27,  35,  42,  52,  65,  77,  88, 102, 119

   9,  13,  18,  24,  35,  43,  52,  62,  77,  89, 102, 116, 135

  14,  20,  27,  35,  40,  50,  61,  73,  90, 104, 119, 135, 148

  20,  26,  35,  43,  50,  60,  73,  85, 104, 118, 135, 151, 166

  27,  35,  42,  52,  61,  73,  84,  98, 119, 135, 150, 168, 185

  35,  43,  52,  62,  73,  85,  98, 112, 135, 151, 168, 186, 205

  44,  54,  65,  77,  90, 104, 119, 135, 144, 162, 181, 201, 222

  54,  64,  77,  89, 104, 118, 135, 151, 162, 180, 201, 221, 244

  65,  77,  88, 102, 119, 135, 150, 168, 181, 201, 220, 242, 267

  77,  89, 102, 116, 135, 151, 168, 186, 201, 221, 242, 264, 291

  90, 104, 119, 135, 148, 166, 185, 205, 222, 244, 267, 291, 312

MATHEMATICA

T[a_, b_]:=((a + b)^2 + 3a + b)/2; A[n_, k_]:=T[BitOr[n, k], BitAnd[n,  k]]; Table[A[n - k, k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, May 21 2017 *)

PROG

(Scheme)

(define (A286099 n) (A286099bi (A002262 n) (A025581 n)))

(define (A286099bi row col) (let ((a (A003986bi row col)) (b (A004198bi row col))) (/ (+ (expt (+ a b) 2) (* 3 a) b) 2))) ;; Here A003986bi and A004198bi implement bitwise-OR (A003986) and bitwise-AND (A004198).

(Python)

def T(a, b): return ((a + b)**2 + 3*a + b)/2

def A(n, k): return T(n|k, n&k)

for n in xrange(0, 21): print [A(k, n - k) for k in xrange(0, n + 1)] # Indranil Ghosh, May 21 2017

CROSSREFS

Cf. A000096 (row 0 & column 0), A162761 (seems to be row 1 & column 1), A046092 (main diagonal).

Cf. A003056, A003986, A004198.

Cf. also arrays A286098, A286101, A286102, A286109.

Sequence in context: A292245 A206427 A112923 * A098366 A284127 A261114

Adjacent sequences:  A286096 A286097 A286098 * A286100 A286101 A286102

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 03 2017

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 16 14:56 EDT 2019. Contains 324152 sequences. (Running on oeis4.)