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 A239662 #25 Nov 08 2024 07:23:47
%S A239662 4,12,20,4,28,0,36,12,44,0,4,52,20,0,60,0,0,68,28,12,76,0,0,4,84,36,0,
%T A239662 0,92,0,20,0,100,44,0,0,108,0,0,12,116,52,28,0,4,124,0,0,0,0,132,60,0,
%U A239662 0,0,140,0,36,20,0,148,68,0,0,0,156,0,0,0,12,164,76,44,0,0,4,172,0,0,28,0,0,180,84,0,0,0,0,188,0,52,0,0,0
%N A239662 Triangle read by rows: T(n,k), n>=1, k>=1, in which column k lists the numbers A017113 interleaved with k-1 zeros, and the first element of column k is in row k(k+1)/2.
%C A239662 Gives an identity for A239050. Alternating sum of row n equals A239050(n), i.e., Sum_{k=1..A003056(n)} (-1)^(k-1)*T(n,k) = 4*A000203(n) = 2*A074400(n) = A239050(n).
%C A239662 Row n has length A003056(n) hence the first element of column k is in row A000217(k).
%C A239662 Note that if T(n,k) = 12 then T(n+1,k+1) = 4, the first element of the column k+1.
%C A239662 The number of positive terms in row n is A001227(n).
%C A239662 For more information see A196020.
%C A239662 Column 1 is A017113. - _Omar E. Pol_, Apr 17 2016
%F A239662 T(n,k) = 2*A236106(n,k) = 4*A196020(n,k).
%e A239662 Triangle begins:
%e A239662 4;
%e A239662 12;
%e A239662 20, 4;
%e A239662 28, 0;
%e A239662 36, 12;
%e A239662 44, 0, 4;
%e A239662 52, 20, 0;
%e A239662 60, 0, 0;
%e A239662 68, 28, 12;
%e A239662 76, 0, 0, 4;
%e A239662 84, 36, 0, 0;
%e A239662 92, 0, 20, 0;
%e A239662 100, 44, 0, 0;
%e A239662 108, 0, 0, 12;
%e A239662 116, 52, 28, 0, 4;
%e A239662 124, 0, 0, 0, 0;
%e A239662 132, 60, 0, 0, 0;
%e A239662 140, 0, 36, 20, 0;
%e A239662 148, 68, 0, 0, 0;
%e A239662 156, 0, 0, 0, 12;
%e A239662 164, 76, 44, 0, 0, 4;
%e A239662 172, 0, 0, 28, 0, 0;
%e A239662 180, 84, 0, 0, 0, 0;
%e A239662 188, 0, 52, 0, 0, 0;
%e A239662 ...
%e A239662 For n = 9, the 9th row of triangle is [68, 28, 12], therefore the alternating row sum is 68 - 28 + 12 = 52. On the other hand we have that 4*A000203(9) = 2*A074400(9) = A239050(9) = 4*13 = 2*26 = 52, equaling the alternating sum of the 9th row of the triangle.
%Y A239662 Cf. A000203, A000217, A003056, A017113, A074400, A196020, A211343, A235791, A236104, A236106, A236112, A237048, A237591, A239050, A239446.
%K A239662 nonn,tabf
%O A239662 1,1
%A A239662 _Omar E. Pol_, Mar 30 2014