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 A059779 #29 Jul 02 2025 16:02:00
%S A059779 2,1,1,3,2,3,4,3,3,4,7,5,6,5,7,11,8,9,9,8,11,18,13,15,14,15,13,18,29,
%T A059779 21,24,23,23,24,21,29,47,34,39,37,38,37,39,34,47,76,55,63,60,61,61,60,
%U A059779 63,55,76,123,89,102,97,99,98,99,97,102,89,123,199,144,165,157,160,159
%N A059779 A Lucas triangle: T(m,n), m >= n >= 0.
%C A059779 From _Amiram Eldar_, May 15 2023: (Start)
%C A059779 Named "Lucas triangle" by Josef (1983), and "Josef's triangle" by Koshy (2007).
%C A059779 The rows of the triangle are the antidiagonals of the array in which the 0th row is T(0, k) = Lucas(k) = A000032(k), the 1st row is T(1, k) = Fibonacci(k+2) = A000045(k+2), and each subsequent row is the sum of the previous 2 rows.
%C A059779 The central elements in the even rows are in A127546, starting from the 2nd row, i.e., the central element of the k-th row, for even k >= 2, is A127546(k/2-1). (End)
%D A059779 Boris A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8.
%H A059779 Boris A. Bondarenko, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/pascal.html">Generalized Pascal Triangles and Pyramids</a>, English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see p. 28.
%H A059779 Alexander Engstrom, <a href="https://arxiv.org/abs/1412.8460">Graph colouring and the total Betti number</a>, arXiv preprint, arXiv:1412.8460 [math.CO], 2014.
%H A059779 Šána Josef, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/21-3/josef.pdf">Lucas Triangle</a>, The Fibonacci Quarterly, Vol. 21, No. 3 (1983), pp. 192-195.
%H A059779 Thomas Koshy, <a href="https://www.jstor.org/stable/40378286">91.01 The central elements in Josef's triangle</a>, The Mathematical Gazette, Vol. 91, No. 520 (2007), pp. 63-68.
%F A059779 T(m, n) = T(m-1, n) + T(m-2, n); T(0, 0)=2, T(1, 0)=1, T(1, 1)=1, T(2, 1)=2.
%e A059779 Triangle starts:
%e A059779 2;
%e A059779 1,1;
%e A059779 3,2,3;
%e A059779 4,3,3,4;
%e A059779 ...
%p A059779 T := proc(m, n) option remember: if m=0 and n=0 then RETURN(2) fi: if m=1 and n=0 then RETURN(1) fi: if m=1 and n=1 then RETURN(1) fi: if m=2 and n=1 then RETURN(2) fi: if m<=n+1 then RETURN(T(m, m-n)) fi: if m<n then RETURN(0) fi: T(m-1,n) + T(m-2,n): end:for m from 0 to 20 do for n from 0 to m do printf(`%d,`,T(m,n)) od: od: # _James Sellers_, Feb 22 2001
%t A059779 T[0, k_] := T[0, k] = LucasL[k]; T[1, k_] := T[1, k] = Fibonacci[k + 2]; T[n_, k_] := T[n, k] = T[n - 1, k] + T[n - 2, k]; Table[T[k, n - k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Amiram Eldar_, May 15 2023 *)
%Y A059779 Cf. A000045, A000032, A127546.
%K A059779 nonn,easy,tabl
%O A059779 0,1
%A A059779 _N. J. A. Sloane_, Feb 22 2001
%E A059779 More terms from _James Sellers_, Feb 22 2001