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

%I A178643 #23 Aug 10 2023 02:16:43
%S A178643 1,10,2,100,19,4,1000,190,36,8,10000,1900,361,68,16,100000,19000,3610,
%T A178643 686,128,32,1000000,190000,36100,6859,1304,240,64,10000000,1900000,
%U A178643 361000,68590,13032,2480,448,128,100000000,19000000,3610000,685900,130321,24760,4720,832,256
%N A178643 Square array read by antidiagonals. Convolution of a(n) = 2*a(n-1) - a(n-2) and 10^n.
%C A178643 Diagonals sum up to A014824.
%C A178643 Alternating diagonal sum gives decimal expansion of fraction 1/119 (A021123).
%H A178643 Robin Visser, <a href="/A178643/b178643.txt">Table of n, a(n) for n = 1..10000</a>
%F A178643 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 A178643 Array starts:
%e A178643      1,    2,    4,    8,
%e A178643     10,   19,   36,   68,
%e A178643    100,  190,  361,  686,
%e A178643   1000, 1900, 3610, 6859,
%o A178643 (Sage)
%o A178643 def a(n,k):
%o A178643     T = [[0 for j in range(k+1)] for i in range(n+1)]
%o A178643     for i in range(n+1): T[i][0] = 10^i
%o A178643     for j in range(1, k+1):
%o A178643         T[0][j] = 2^j
%o A178643         for i in range(1, n+1): T[i][j] = 2*T[i][j-1] - T[i-1][j-1]
%o A178643     return T[n][k]  # _Robin Visser_, Aug 09 2023
%Y A178643 Cf. A014824, A000129, A021123, A021083, A178511.
%K A178643 easy,nonn,tabl
%O A178643 1,2
%A A178643 _Mark Dols_, May 31 2010
%E A178643 More terms from _Robin Visser_, Aug 09 2023