A383414 Array read by ascending antidiagonals: A(n,k) = 4^n*(8*k + 7).

7, 28, 15, 112, 60, 23, 448, 240, 92, 31, 1792, 960, 368, 124, 39, 7168, 3840, 1472, 496, 156, 47, 28672, 15360, 5888, 1984, 624, 188, 55, 114688, 61440, 23552, 7936, 2496, 752, 220, 63, 458752, 245760, 94208, 31744, 9984, 3008, 880, 252, 71, 1835008, 983040, 376832, 126976, 39936, 12032, 3520, 1008, 284, 79

Offset: 0

Author

Stefano Spezia, Apr 26 2025

Keywords

• nonn
• easy
• tabl

Examples

			The array begins as:
      7,    15,    23,     31,     39,     47, ...
     28,    60,    92,    124,    156,    188, ...
    112,   240,   368,    496,    624,    752, ...
    448,   960,  1472,   1984,   2496,   3008, ...
   1792,  3840,  5888,   7936,   9984,  12032, ...
   7168, 15360, 23552,  31744,  39936,  48128, ...
  28672, 61440, 94208, 126976, 159744, 192512, ...
  ...
		

References

• G. H. Hardy, Ramanujan: twelve lectures on subjects suggested by his life and work, Cambridge, University Press, 1940, p. 12.
• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, pages 246-247.

Crossrefs

Cf. A000302, A004215, A383415 (antidiagonal sums).

Row n=0 gives A004771.

Column k=0 gives A002042.

Programs

Mathematica

A[n_,k_]:=4^n(8k+7); Table[A[n-k,k],{n,0,9},{k,0,n}]//Flatten

Formula

A(n,k) = A000302(n)*A004771(k).

G.f.: (7 + y)/((1 - 4*x)*(1 - y)^2).

E.g.f.: exp(4*x+y)*(7 + 8*y).