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A277046 Triangle read by rows: T(n,k) = 2^n - n + k - 1 for n >= 1, with 1 <= k <= 2n-1. 2

%I #55 Nov 27 2021 12:37:04

%S 1,2,3,4,5,6,7,8,9,12,13,14,15,16,17,18,27,28,29,30,31,32,33,34,35,58,

%T 59,60,61,62,63,64,65,66,67,68,121,122,123,124,125,126,127,128,129,

%U 130,131,132,133,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519

%N Triangle read by rows: T(n,k) = 2^n - n + k - 1 for n >= 1, with 1 <= k <= 2n-1.

%H Harvey P. Dale, <a href="/A277046/b277046.txt">Table of n, a(n) for n = 1..1000</a>

%e Triangle begins:

%e 1;

%e 2, 3, 4;

%e 5, 6, 7, 8, 9;

%e 12, 13, 14, 15, 16, 17, 18;

%e 27, 28, 29, 30, 31, 32, 33, 34, 35;

%e 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68;

%e ...

%e Written as an isosceles triangle the sequence begins:

%e . 1;

%e . 2, 3, 4;

%e . 5, 6, 7, 8, 9;

%e . 12, 13, 14, 15, 16, 17, 18;

%e . 27, 28, 29, 30, 31, 32, 33, 34, 35;

%e . 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68;

%e ..

%t Table[2^n-n+k-1,{n,10},{k,2n-1}]//Flatten (* _Harvey P. Dale_, Nov 27 2021 *)

%Y Row lengths are A005408.

%Y Row sums give A118414.

%Y Column 1 gives A000325, n>=1.

%Y Middle diagonal gives A000225.

%Y Right border gives A083706.

%Y Cf. A118413.

%K nonn,tabf

%O 1,2

%A _Miquel Cerda_, Sep 27 2016

%E Definition from _Omar E. Pol_, Sep 28 2016

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)