A178643 Square array read by antidiagonals. Convolution of a(n) = 2*a(n-1) - a(n-2) and 10^n.

1, 10, 2, 100, 19, 4, 1000, 190, 36, 8, 10000, 1900, 361, 68, 16, 100000, 19000, 3610, 686, 128, 32, 1000000, 190000, 36100, 6859, 1304, 240, 64, 10000000, 1900000, 361000, 68590, 13032, 2480, 448, 128, 100000000, 19000000, 3610000, 685900, 130321, 24760, 4720, 832, 256

Offset: 1

Author

Mark Dols, May 31 2010

Keywords

• easy
• nonn
• tabl

Comments

Diagonals sum up to A014824.

Alternating diagonal sum gives decimal expansion of fraction 1/119 (A021123).

Examples

			Array starts:
     1,    2,    4,    8,
    10,   19,   36,   68,
   100,  190,  361,  686,
  1000, 1900, 3610, 6859,
		

Links

• Robin Visser, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014824, A000129, A021123, A021083, A178511.

Programs

Sage

def a(n,k):
    T = [[0 for j in range(k+1)] for i in range(n+1)]
    for i in range(n+1): T[i][0] = 10^i
    for j in range(1, k+1):
        T[0][j] = 2^j
        for i in range(1, n+1): T[i][j] = 2*T[i][j-1] - T[i-1][j-1]
    return T[n][k]  # Robin Visser, Aug 09 2023

Formula

T(n,k) = 2*T(n,k-1) - T(n-1,k-1) for all n, k > 0, where T(n,0) = 10^n and T(0,k) = 2^k. - Robin Visser, Aug 09 2023

Extensions

More terms from Robin Visser, Aug 09 2023