The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A104746

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A104746

Array T(n,k) read by antidiagonals: T(1,k) = 2^k-1 and recursively T(n,k) = T(n-1,k) + A000337(k-1), n,k >= 1.
(history; published version)

#17 by Michel Marcus at Sat Mar 30 07:53:17 EDT 2024

STATUS

reviewed

approved

#16 by Joerg Arndt at Sat Mar 30 07:06:22 EDT 2024

STATUS

proposed

reviewed

#15 by Jean-François Alcover at Sat Mar 30 06:44:51 EDT 2024

STATUS

editing

proposed

#14 by Jean-François Alcover at Sat Mar 30 06:43:28 EDT 2024

DATA

1, 1, 3, 1, 4, 7, 1, 5, 12, 15, 1, 6, 17, 32, 31, 1, 7, 22, 49, 80, 63, 1, 8, 27, 66, 129, 192, 127, 1, 9, 32, 83, 178, 321, 448, 255, 1, 10, 37, 100, 227, 450, 769, 1024, 511, 1, 11, 42, 117, 276, 579, 1090, 1793, 2304, 1023, 1, 12, 47, 134, 325, 708, 1411, 2562, 4097, 5120, 2047, 1, 13, 52, 151, 374, 837, 1732, 3331, 5890, 9217, 11264, 4095

MATHEMATICA

A000337[n_] := (n - 1)*2^n + 1;

T[1, k_] := 2^k - 1;

T[n_, k_] := T[n, k] = T[n - 1, k] + A000337[k - 1];

Table[T[n - k + 1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 30 2024 *)

STATUS

approved

editing

Discussion

Sat Mar 30

06:44

Jean-François Alcover: Completed last antidiagonal in data section

#13 by Michael De Vlieger at Sun Feb 13 23:17:55 EST 2022

STATUS

proposed

approved

#12 by Jon E. Schoenfield at Sun Feb 13 22:43:47 EST 2022

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Sun Feb 13 22:43:45 EST 2022

NAME

Array T(n,k) read by antidiagonals: T(1,k) = 2^k-1 and recursively T(n,k) = T(n-1,k) + A000337(k-1), n,k >= 1.

COMMENTS

Generally, row n of the array is the binomial transform for 0, 1, n, 2n - 1, 3n-2, 4n-3, ...

FORMULA

T(2,k) = A001787(k), binomial transform of 0, 1, 2, 3, 4, 5, 6, ...

T(3,k) = A000337(k), binomial transform of 0, 1, 3, 5, 7, 9, 11, ...

T(4,k) = A027992(k-1), binomial transform of 0, 1, 4, 7, 10, 13, 16, 19, 22, 25, ...

T(5,k) = binomial transform of 0, 1, 5, 9, 13, 17, 21, 25, 29, ...

EXAMPLE

To the first row, add the terms 0, 1, 5, 17, 49, 129, ... as indicated:

1, 3, 7, 15, 31, 63, ...

0, 1, 5, 17, 49, 129, ... (getting row 2 of the array:

1, 4 , 12, 32, 80, 192, ... (= A001787, binomial transform for 1,2,3, ...)

1, 3, 7, 15, 31, 63, ...

1, 4, 12, 32, 80, 192, ...

1, 5, 17, 49, 129, 321, ...

1, 6, 22, 66, 178, 450, ...

STATUS

approved

editing

#10 by Alois P. Heinz at Mon Feb 01 22:32:39 EST 2021

STATUS

editing

approved

#9 by Alois P. Heinz at Mon Feb 01 22:32:37 EST 2021

EXTENSIONS

Terms corrected by _R. J. Mathar, _, Oct 30 2011

STATUS

approved

editing

#8 by Joerg Arndt at Mon Jul 02 14:09:07 EDT 2012

STATUS

proposed

approved