cp's OEIS Frontend

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.

%I A349890 #14 Jan 18 2022 21:45:22
%S A349890 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,
%T A349890 20,14,43,42,40,37,33,28,22,15,59,58,56,53,49,44,38,31,23,75,74,72,69,
%U A349890 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
%N 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.
%C A349890 Conjecture: The terms of the triangle yield a permutation of the positive integers (A000027).
%F A349890 T(2^n, 1) = A007583(n) for n >= 0.
%F A349890 T(n, 1) - T(n, n) = A000217(n-1) for n > 0.
%F A349890 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).
%e A349890 The triangle T(n, k) for 1 <= k <= n begins:
%e A349890 n\k:   1   2   3   4   5   6   7   8   9  10  11
%e A349890 ================================================
%e A349890 01 :   1
%e A349890 02 :   3   2
%e A349890 03 :   7   6   4
%e A349890 04 :  11  10   8   5
%e A349890 05 :  19  18  16  13   9
%e A349890 06 :  27  26  24  21  17  12
%e A349890 07 :  35  34  32  29  25  20  14
%e A349890 08 :  43  42  40  37  33  28  22  15
%e A349890 09 :  59  58  56  53  49  44  38  31  23
%e A349890 10 :  75  74  72  69  65  60  54  47  39  30
%e A349890 11 :  91  90  88  85  81  76  70  63  55  46  36
%e A349890 etc.
%o A349890 (PARI) T(n,k) = my(e=1+logint(n,2)); n*2^e - (4^e-1)/3 - k*(k-1)/2;
%o A349890 row(n) = vector(n, k, T(n,k)); \\ _Michel Marcus_, Dec 05 2021
%Y A349890 Cf. A000027, A000217, A007583.
%K A349890 nonn,easy,tabl
%O A349890 1,2
%A A349890 _Werner Schulte_, Dec 04 2021