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A283943 Interspersion of the signature sequence of e (a rectangular array, by antidiagonals). 1
1, 4, 2, 10, 6, 3, 19, 13, 8, 5, 30, 23, 16, 11, 7, 44, 35, 27, 20, 14, 9, 61, 50, 40, 32, 24, 17, 12, 81, 68, 56, 46, 37, 28, 21, 15, 103, 89, 75, 63, 52, 42, 33, 25, 18, 128, 112, 97, 83, 70, 58, 48, 38, 29, 22, 156, 138, 121, 106, 91, 77, 65, 54, 43, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row n is the ordered sequence of numbers k such that A023123(k) = n. As a sequence, A283943 is a permutation of the positive integers. This is a transposable interspersion; i.e., every row intersperses all other rows, and every column intersperses all other columns.

LINKS

Clark Kimberling, Antidiagonals n = 1..60, flattened

Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.

EXAMPLE

Northwest corner:

1  4   10  19  30  44  61  81   103

2  6   13  23  35  50  68  89   112

3  8   16  27  40  56  75  97   121

5  11  20  32  46  63  83  106  131

7  14  23  37  52  70  91  115  141

9  17  28  42  58  77  99  124  151

MATHEMATICA

r = E; z = 100; s[0] = 1; s[n_] := s[n] = s[n - 1] + 1 + Floor[n*r];

u = Table[n + 1 + Sum[Floor[(n - k)/r], {k, 0, n}], {n, 0, z}] (* A022786, col 1 of A283943 *)

v = Table[s[n], {n, 0, z}] (* A022785, row 1 of A283943*)

w[i_, j_] := u[[i]] + v[[j]] + (i - 1)*(j - 1) - 1;

Grid[Table[w[i, j], {i, 1, 10}, {j, 1, 10}]] (*A 283943, array*)

Flatten[Table[w[k, n - k + 1], {n, 1, 20}, {k, 1, n}]] (* A283943, sequence*)

PROG

(PARI)

\\ Produces the triangle when the array is read by antidiagonals

r = exp(1);

z = 100;

s(n) = if(n<1, 1, s(n - 1) + 1 + floor(n*r));

p(n) = n + 1 + sum(k=0, n, floor((n - k)/r));

u = v = vector(z + 1);

for(n=1, 101, (v[n] = s(n - 1)));

for(n=1, 101, (u[n] = p(n - 1)));

w(i, j) = u[i] + v[j] + (i - 1) * (j - 1) - 1;

tabl(nn) = {for(n=1, nn, for(k=1, n, print1(w(k, n - k + 1), ", "); ); print(); ); };

tabl(10) \\ Indranil Ghosh, Mar 26 2017

(Python)

# Produces the triangle when the array is read by antidiagonals

import math

from mpmath import *

mp.dps = 100

def s(n): return 1 if n<1 else s(n - 1) + 1 + int(math.floor(n*e))

def p(n): return n + 1 + sum([int(math.floor((n - k)/e)) for k in range(0, n+1)])

v=[s(n) for n in range(0, 101)]

u=[p(n) for n in range(0, 101)]

def w(i, j): return u[i - 1] + v[j - 1] + (i - 1) * (j - 1) - 1

for n in range(1, 11):

....print [w(k, n - k + 1) for k in range(1, n + 1)] # Indranil Ghosh, Mar 26 2017

CROSSREFS

Cf. A001113, A023123, A022786, A022785.

Sequence in context: A198326 A309989 A283938 * A283942 A266418 A193422

Adjacent sequences:  A283940 A283941 A283942 * A283944 A283945 A283946

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Mar 26 2017

STATUS

approved

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Last modified August 7 11:38 EDT 2022. Contains 355985 sequences. (Running on oeis4.)