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A173787 Triangle read by rows: T(n,k) = 2^n - 2^k, 0 <= k <= n.

%I A173787 #16 Sep 08 2022 08:45:50
%S A173787 0,1,0,3,2,0,7,6,4,0,15,14,12,8,0,31,30,28,24,16,0,63,62,60,56,48,32,
%T A173787 0,127,126,124,120,112,96,64,0,255,254,252,248,240,224,192,128,0,511,
%U A173787 510,508,504,496,480,448,384,256,0,1023,1022,1020,1016,1008,992,960,896,768,512,0
%N A173787 Triangle read by rows: T(n,k) = 2^n - 2^k, 0 <= k <= n.
%H A173787 G. C. Greubel, <a href="/A173787/b173787.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A173787 A000120(T(n,k)) = A025581(n,k).
%F A173787 Row sums give A000337.
%F A173787 Central terms give A020522.
%F A173787 T(2*n+1, n) = A006516(n+1).
%F A173787 T(2*n+3, n+2) = A059153(n).
%F A173787 T(n, k) = A140513(n,k) - A173786(n,k), 0 <= k <= n.
%F A173787 T(n, k) = A173786(n,k) - A059268(n+1,k+1), 0 < k <= n.
%F A173787 T(2*n, 2*k) = T(n,k) * A173786(n,k), 0 <= k <= n.
%F A173787 T(n, 0) = A000225(n).
%F A173787 T(n, 1) = A000918(n) for n>0.
%F A173787 T(n, 2) = A028399(n) for n>1.
%F A173787 T(n, 3) = A159741(n-3) for n>3.
%F A173787 T(n, 4) = A175164(n-4) for n>4.
%F A173787 T(n, 5) = A175165(n-5) for n>5.
%F A173787 T(n, 6) = A175166(n-6) for n>6.
%F A173787 T(n, n-4) = A110286(n-4) for n>3.
%F A173787 T(n, n-3) = A005009(n-3) for n>2.
%F A173787 T(n, n-2) = A007283(n-2) for n>1.
%F A173787 T(n, n-1) = A000079(n-1) for n>0.
%F A173787 T(n, n) = A000004(n).
%e A173787 Triangle begins as:
%e A173787    0;
%e A173787    1,  0;
%e A173787    3,  2,  0;
%e A173787    7,  6,  4,  0;
%e A173787   15, 14, 12,  8,  0;
%e A173787   31, 30, 28, 24, 16, 0;
%t A173787 Table[2^n -2^k, {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jul 13 2021 *)
%o A173787 (Magma) [2^n -2^k: k in [0..n], n in [0..15]]; // _G. C. Greubel_, Jul 13 2021
%o A173787 (Sage) flatten([[2^n -2^k for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Jul 13 2021
%K A173787 nonn,easy,tabl
%O A173787 0,4
%A A173787 _Reinhard Zumkeller_, Feb 28 2010