%I #24 Sep 22 2025 16:01:03

%S 1,10,2,100,19,4,1000,190,36,8,10000,1900,361,68,16,100000,19000,3610,

%T 686,128,32,1000000,190000,36100,6859,1304,240,64,10000000,1900000,

%U 361000,68590,13032,2480,448,128,100000000,19000000,3610000,685900,130321,24760,4720,832,256

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

%C Diagonals sum up to A014824.

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

%H Robin Visser, <a href="/A178643/b178643.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%e Array starts:

%e 1, 2, 4, 8,

%e 10, 19, 36, 68,

%e 100, 190, 361, 686,

%e 1000, 1900, 3610, 6859,

%o (SageMath)

%o def a(n,k):

%o T = [[0 for j in range(k+1)] for i in range(n+1)]

%o for i in range(n+1): T[i][0] = 10^i

%o for j in range(1, k+1):

%o T[0][j] = 2^j

%o for i in range(1, n+1): T[i][j] = 2*T[i][j-1] - T[i-1][j-1]

%o return T[n][k] # _Robin Visser_, Aug 09 2023

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

%K easy,nonn,tabl

%O 1,2

%A _Mark Dols_, May 31 2010

%E More terms from _Robin Visser_, Aug 09 2023