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A349890 Triangle read by rows: T(n,k) = n * 2^e(n) - (4^e(n) - 1) / 3 - k * (k - 1) / 2 with e(n) = 1 + floor(log_2(n)) for n >= 1 and 1 <= k <= n. 0
1, 3, 2, 7, 6, 4, 11, 10, 8, 5, 19, 18, 16, 13, 9, 27, 26, 24, 21, 17, 12, 35, 34, 32, 29, 25, 20, 14, 43, 42, 40, 37, 33, 28, 22, 15, 59, 58, 56, 53, 49, 44, 38, 31, 23, 75, 74, 72, 69, 65, 60, 54, 47, 39, 30, 91, 90, 88, 85, 81, 76, 70, 63, 55, 46, 36, 107, 106, 104, 101, 97, 92, 86, 79, 71, 62, 52, 41 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Conjecture: The terms of the triangle yield a permutation of the positive integers (A000027).

LINKS

Table of n, a(n) for n=1..78.

FORMULA

T(2^n, 1) = A007583(n) for n >= 0.

T(n, 1) - T(n, n) = A000217(n-1) for n > 0.

T(n, k) = T(n-1, k) + T(n-1, k-1) - T(n-1-2^(e(n-1)-e(n-2)), k-1) with e(n) = 1 + floor(log_2(n)) for n > 3 and 1 < k < n-1 (conjectured).

EXAMPLE

The triangle T(n, k) for 1 <= k <= n begins:

n\k:   1   2   3   4   5   6   7   8   9  10  11

================================================

01 :   1

02 :   3   2

03 :   7   6   4

04 :  11  10   8   5

05 :  19  18  16  13   9

06 :  27  26  24  21  17  12

07 :  35  34  32  29  25  20  14

08 :  43  42  40  37  33  28  22  15

09 :  59  58  56  53  49  44  38  31  23

10 :  75  74  72  69  65  60  54  47  39  30

11 :  91  90  88  85  81  76  70  63  55  46  36

etc.

PROG

(PARI) T(n, k) = my(e=1+logint(n, 2)); n*2^e - (4^e-1)/3 - k*(k-1)/2;

row(n) = vector(n, k, T(n, k)); \\ Michel Marcus, Dec 05 2021

CROSSREFS

Cf. A000027, A000217, A007583.

Sequence in context: A268832 A201566 A072764 * A130328 A228993 A083569

Adjacent sequences:  A349887 A349888 A349889 * A349891 A349892 A349893

KEYWORD

nonn,easy,tabl

AUTHOR

Werner Schulte, Dec 04 2021

STATUS

approved

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Last modified September 25 22:56 EDT 2022. Contains 356986 sequences. (Running on oeis4.)