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A360033 Table T(n,k), n >= 1 and k >= 0, read by antidiagonals, related to Jacobsthal numbers A001045.

%I A360033 #11 Feb 04 2023 11:10:11
%S A360033 1,2,1,3,3,3,4,5,7,5,5,7,11,13,11,6,9,15,21,27,21,7,11,19,29,43,53,43,
%T A360033 8,13,23,37,59,85,107,85,9,15,27,45,75,117,171,213,171,10,17,31,53,91,
%U A360033 149,235,341,427,341,11,19,35,61,107,181,299,469
%N A360033 Table T(n,k), n >= 1 and k >= 0, read by antidiagonals, related to Jacobsthal numbers A001045.
%F A360033 T(n,k) = T(1,k) + (n-1)*2^k.
%F A360033 T(n,k) = 2*T(n, k-1) + (-1)^k.
%F A360033 T(n,k) = T(n-1,k) + 2^k.
%F A360033 T(n,k) = 2^k * n - A001045(k).
%F A360033 T(n,k) = T(n,k-1) +2*T(n,k-2).
%e A360033 The array T(n,k), for n <= 1 and k >= 0, begins:
%e A360033 n = 1: 1,  1,  3,  5,  11,  21,  43, ... -> A001045(k+1)
%e A360033 n = 2: 2,  3,  7, 13,  27,  53, 107, ... -> A048573(k)
%e A360033 n = 3: 3,  5, 11, 21,  43,  85, 171, ... -> A001045(k+3)
%e A360033 n = 4: 4,  7, 15, 29,  59, 117, 235, ... -> ?
%e A360033 n = 5: 5,  9, 19, 37,  75, 149, 299, ... -> A062092(k+1)
%e A360033 n = 6: 6, 11, 23, 45,  91, 181, 363, ... -> ?
%e A360033 n = 7: 7, 13, 27, 53, 107, 213, 427, ... -> A048573(k+2)
%Y A360033 Cf. A001045, A048573, A062092.
%Y A360033 Columns: A000027, A005408, A004767, A004770, A106839 for k = 0, 1, 2, 3, 4.
%K A360033 nonn,tabl,easy
%O A360033 1,2
%A A360033 _Philippe Deléham_, Jan 22 2023