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A104793 Triangle T(n,k) = A023537(n-k), n >= 1, 0 <= k < n, read by rows.

%I A104793 #15 Jan 07 2025 16:52:03
%S A104793 1,5,1,13,5,1,28,13,5,1,54,28,13,5,1,98,54,28,13,5,1,171,98,54,28,13,
%T A104793 5,1,291,171,98,54,28,13,5,1,487,291,171,98,54,28,13,5,1,806,487,291,
%U A104793 171,98,54,28,13,5,1,1324,806,487,291,171,98,54,28,13,5,1
%N A104793 Triangle T(n,k) = A023537(n-k), n >= 1, 0 <= k < n, read by rows.
%C A104793 Repeatedly writing the sequence A023537 backwards.
%H A104793 G. C. Greubel, <a href="/A104793/b104793.txt">Rows n = 1..100 of triangle, flattened</a>
%F A104793 From _Ralf Stephan_, Apr 05 2009: (Start)
%F A104793 T(n,k) = Lucas(n-k+4) - (3*n - 3*k + 7).
%F A104793 T(n,k) = A023537(A004736(n, k+1)). (End)
%e A104793 First few rows of the triangle are:
%e A104793    1;
%e A104793    5,  1;
%e A104793   13,  5,  1;
%e A104793   28, 13,  5,  1;
%e A104793   54, 28, 13,  5, 1;
%e A104793   98, 54, 28, 13, 5, 1; ...
%t A104793 Table[LucasL[n-k+4] -3*n+3*k-7, {n,1,12}, {k,0,n-1}]//Flatten (* _G. C. Greubel_, Jun 01 2019 *)
%o A104793 (PARI) {T(n,k) = fibonacci(n-k+5) + fibonacci(n-k+3) -3*n +3*k - 7}; \\ _G. C. Greubel_, Jun 01 2019
%o A104793 (Magma) [[Lucas(n-k+4) -(3*n-3*k+7): k in [0..n-1]]: n in [1..12]]; // _G. C. Greubel_, Jun 01 2019
%o A104793 (Sage) [[lucas_number2(n-k+4, 1, -1) -3*n+3*k-7 for k in (0..n-1)] for n in (1..12)] # _G. C. Greubel_, Jun 01 2019
%o A104793 (GAP) Flat(List([1..12], n-> List([0..n-1], k-> Lucas(1, -1, n-k+4)[2] -3*n+3*k-7 ))); # _G. C. Greubel_, Jun 01 2019
%Y A104793 Row sums are in A027963.
%Y A104793 Cf. A104765.
%K A104793 nonn,tabl
%O A104793 1,2
%A A104793 _Gary W. Adamson_, Mar 26 2005
%E A104793 Edited by _Ralf Stephan_, Apr 05 2009