This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A176794 #9 Oct 04 2024 07:41:06
%S A176794 1,1,1,1,17,1,1,129,129,1,1,833,1025,833,1,1,5121,6657,6657,5121,1,1,
%T A176794 30977,40961,43265,40961,30977,1,1,186369,247809,266241,266241,247809,
%U A176794 186369,1,1,1119233,1490945,1610753,1638401,1610753,1490945,1119233,1
%N A176794 Triangle read by rows: T(n, k) = 2^n*(q^k - 1)*(q^(n - k) - 1) + 1, where q = 3.
%H A176794 G. C. Greubel, <a href="/A176794/b176794.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A176794 T(n, k) = 1 - (f(n+1, 2*k+1, q) - f(n+1, 1, q)) - (f(n+1, 2*n-2*k+1, q) - f(n+1, 2*n+1, q)), where f(n, k, q) = 2^(n-1) * q^((k-1)/2), and q = 3.
%F A176794 From _G. C. Greubel_, Oct 02 2024: (Start)
%F A176794 T(n, k) = 2^n*(3^k - 1)*(3^(n-k) - 1) + 1.
%F A176794 T(2*n, n) = 1 + 4^n*(3^n - 1)^2 = 1 + 16*A144843(n).
%F A176794 Sum_{k=0..n} T(n, k) = 2^n*(n + 2 + (n-2)*3^n) + (n+1).
%F A176794 Sum_{k=0..n} (-1)^k*T(n, k) = (1/4)*(1 + (-1)^n)*(2 + 2^n - 6^n). (End)
%e A176794 Triangle begins as:
%e A176794 1;
%e A176794 1, 1;
%e A176794 1, 17, 1;
%e A176794 1, 129, 129, 1;
%e A176794 1, 833, 1025, 833, 1;
%e A176794 1, 5121, 6657, 6657, 5121, 1;
%e A176794 1, 30977, 40961, 43265, 40961, 30977, 1;
%e A176794 1, 186369, 247809, 266241, 266241, 247809, 186369, 1;
%e A176794 1, 1119233, 1490945, 1610753, 1638401, 1610753, 1490945, 1119233, 1;
%t A176794 T[n_, k_, q_] := 2^n*(q^k - 1)*(q^(n - k) - 1) + 1;
%t A176794 Table[T[n,k,3], {n,0,12}, {k,0,n}]//Flatten
%o A176794 (Magma)
%o A176794 f:= func< n,k,q | 1 + (q^k-1)*(q^(n-k)-1)*2^n >;
%o A176794 A176794:= func< n,k | f(n,k,3) >;
%o A176794 [A176794(n,k): k in [0..n], n in [0..13]]; // _G. C. Greubel_, Oct 03 2024
%o A176794 (SageMath)
%o A176794 def f(n, k, q): return 1 + (q^k -1)*(q^(n-k) -1)*2^n
%o A176794 def A176794(n,k): return f(n,k,3)
%o A176794 flatten([[A176794(n, k) for k in range(n+1)] for n in range(14)]) # _G. C. Greubel_, Oct 03 2024
%Y A176794 Cf. A000012 (q=1), A176793 (q=2), this sequence (q=3), A176795 (q=4).
%Y A176794 Cf. A144843.
%K A176794 nonn,tabl
%O A176794 0,5
%A A176794 _Roger L. Bagula_, Apr 26 2010
%E A176794 Edited by _G. C. Greubel_, Oct 03 2024