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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.

%I A277046 #55 Nov 27 2021 12:37:04
%S A277046 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 A277046 59,60,61,62,63,64,65,66,67,68,121,122,123,124,125,126,127,128,129,
%U A277046 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 A277046 Triangle read by rows: T(n,k) = 2^n - n + k - 1 for n >= 1, with 1 <= k <= 2n-1.
%H A277046 Harvey P. Dale, <a href="/A277046/b277046.txt">Table of n, a(n) for n = 1..1000</a>
%e A277046 Triangle begins:
%e A277046 1;
%e A277046 2,   3,  4;
%e A277046 5,   6,  7,  8,  9;
%e A277046 12, 13, 14, 15, 16, 17, 18;
%e A277046 27, 28, 29, 30, 31, 32, 33, 34, 35;
%e A277046 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68;
%e A277046 ...
%e A277046 Written as an isosceles triangle the sequence begins:
%e A277046 .                      1;
%e A277046 .                  2,  3,  4;
%e A277046 .              5,  6,  7,  8,  9;
%e A277046 .         12, 13, 14, 15, 16, 17, 18;
%e A277046 .     27, 28, 29, 30, 31, 32, 33, 34, 35;
%e A277046 . 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68;
%e A277046 ..
%t A277046 Table[2^n-n+k-1,{n,10},{k,2n-1}]//Flatten (* _Harvey P. Dale_, Nov 27 2021 *)
%Y A277046 Row lengths are A005408.
%Y A277046 Row sums give A118414.
%Y A277046 Column 1 gives A000325, n>=1.
%Y A277046 Middle diagonal gives A000225.
%Y A277046 Right border gives A083706.
%Y A277046 Cf. A118413.
%K A277046 nonn,tabf
%O A277046 1,2
%A A277046 _Miquel Cerda_, Sep 27 2016
%E A277046 Definition from _Omar E. Pol_, Sep 28 2016