cp's OEIS Frontend

A158753 Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.

%I A158753 #7 Sep 08 2022 08:45:43
%S A158753 1,4,1,11,4,1,29,11,4,1,76,29,11,4,1,199,76,29,11,4,1,521,199,76,29,
%T A158753 11,4,1,1364,521,199,76,29,11,4,1,3571,1364,521,199,76,29,11,4,1,9349,
%U A158753 3571,1364,521,199,76,29,11,4,1,24476,9349,3571,1364,521,199,76,29,11,4,1
%N A158753 Triangle T(n, k) = A000032(2*(n-k) + 1), read by rows.
%D A158753 H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, NY, 1973, pp. 159-162.
%H A158753 G. C. Greubel, <a href="/A158753/b158753.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A158753 T(n, k) = 5*e(n, k), where e(n,k) = (e(n-1, k)*e(n, k-1) + 1)/e(n-1, k-1), and e(n, 0) = GoldenRatio^(n) + GoldenRatio^(-n).
%F A158753 Sum_{k=0..n} T(n, k) = A004146(n-1).
%F A158753 T(n, k) = A000032(2*(n-k) + 1). - _G. C. Greubel_, Dec 06 2021
%e A158753 Triangle begins as:
%e A158753      1;
%e A158753      4,   1;
%e A158753     11,   4,   1;
%e A158753     29,  11,   4,  1;
%e A158753     76,  29,  11,  4,  1;
%e A158753    199,  76,  29, 11,  4,  1;
%e A158753    521, 199,  76, 29, 11,  4,  1;
%e A158753   1364, 521, 199, 76, 29, 11,  4,  1;
%t A158753 Table[LucasL[2*(n-k) + 1], {n, 2, 16}, {k, 2, n}]//Flatten (* _G. C. Greubel_, Dec 06 2021 *)
%o A158753 (Magma) [Lucas(2*n-2*k+1): k in [2..n], n in [2..16]]; // _G. C. Greubel_, Dec 06 2021
%o A158753 (Sage) flatten([[lucas_number2(2*(n-k)+1, 1, -1) for k in (2..n)] for n in (2..16)]) # _G. C. Greubel_, Dec 06 2021
%Y A158753 Cf. A000032, A002878, A004146, A158786.
%K A158753 nonn,tabl
%O A158753 2,2
%A A158753 _Roger L. Bagula_ and _Gary W. Adamson_, Mar 25 2009
%E A158753 Edited by _G. C. Greubel_, Dec 06 2021