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 A383414 #9 Jul 22 2025 15:49:58
%S A383414 7,28,15,112,60,23,448,240,92,31,1792,960,368,124,39,7168,3840,1472,
%T A383414 496,156,47,28672,15360,5888,1984,624,188,55,114688,61440,23552,7936,
%U A383414 2496,752,220,63,458752,245760,94208,31744,9984,3008,880,252,71,1835008,983040,376832,126976,39936,12032,3520,1008,284,79
%N A383414 Array read by ascending antidiagonals: A(n,k) = 4^n*(8*k + 7).
%D A383414 G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 12.
%D A383414 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 246-247.
%F A383414 A(n,k) = A000302(n)*A004771(k).
%F A383414 G.f.: (7 + y)/((1 - 4*x)*(1 - y)^2).
%F A383414 E.g.f.: exp(4*x+y)*(7 + 8*y).
%e A383414 The array begins as:
%e A383414 7, 15, 23, 31, 39, 47, ...
%e A383414 28, 60, 92, 124, 156, 188, ...
%e A383414 112, 240, 368, 496, 624, 752, ...
%e A383414 448, 960, 1472, 1984, 2496, 3008, ...
%e A383414 1792, 3840, 5888, 7936, 9984, 12032, ...
%e A383414 7168, 15360, 23552, 31744, 39936, 48128, ...
%e A383414 28672, 61440, 94208, 126976, 159744, 192512, ...
%e A383414 ...
%t A383414 A[n_,k_]:=4^n(8k+7); Table[A[n-k,k],{n,0,9},{k,0,n}]//Flatten
%Y A383414 Cf. A000302, A004215, A383415 (antidiagonal sums).
%Y A383414 Row n=0 gives A004771.
%Y A383414 Column k=0 gives A002042.
%K A383414 nonn,easy,tabl
%O A383414 0,1
%A A383414 _Stefano Spezia_, Apr 26 2025