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A106262 An invertible triangle of remainders of 2^n.

%I A106262 #12 Jan 11 2023 15:59:46
%S A106262 1,0,1,0,2,1,0,1,2,1,0,2,0,2,1,0,1,0,4,2,1,0,2,0,3,4,2,1,0,1,0,1,2,4,
%T A106262 2,1,0,2,0,2,4,1,4,2,1,0,1,0,4,2,2,0,4,2,1,0,2,0,3,4,4,0,8,4,2,1,0,1,
%U A106262 0,1,2,1,0,7,8,4,2,1,0,2,0,2,4,2,0,5,6,8,4,2,1,0,1,0,4,2,4,0,1,2,5,8,4,2,1
%N A106262 An invertible triangle of remainders of 2^n.
%H A106262 G. C. Greubel, <a href="/A106262/b106262.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A106262 T(n, k) = 2^(n-k) mod (k+2).
%F A106262 Sum_{k=0..n} T(n, k) = A106263(n) (row sums).
%F A106262 Sum_{k=0..floor(n/2)} T(n-k, k) = A106264(n) (diagonal sums).
%F A106262 From _G. C. Greubel_, Jan 10 2023: (Start)
%F A106262 T(n, 0) = A000007(n).
%F A106262 T(n, 1) = A000034(n+1).
%F A106262 T(2*n, n) = A213859(n).
%F A106262 T(2*n, n-1) = A015910(n+1).
%F A106262 T(2*n, n+1) = A294390(n+3).
%F A106262 T(2*n+1, n-1) = A112983(n+1).
%F A106262 T(2*n+1, n+1) = A294389(n+3).
%F A106262 T(2*n-1, n-1) = A062173(n+1). (End)
%e A106262 Triangle begins:
%e A106262   1;
%e A106262   0, 1;
%e A106262   0, 2, 1;
%e A106262   0, 1, 2, 1;
%e A106262   0, 2, 0, 2, 1;
%e A106262   0, 1, 0, 4, 2, 1;
%e A106262   0, 2, 0, 3, 4, 2, 1;
%e A106262   0, 1, 0, 1, 2, 4, 2, 1;
%e A106262   0, 2, 0, 2, 4, 1, 4, 2, 1;
%e A106262   0, 1, 0, 4, 2, 2, 0, 4, 2, 1;
%t A106262 Table[PowerMod[2, n-k, k+2], {n,0,15}, {k,0,n}]//Flatten (* _G. C. Greubel_, Jan 10 2023 *)
%o A106262 (Magma) [Modexp(2, n-k, k+2): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Jan 10 2023
%o A106262 (SageMath) flatten([[power_mod(2,n-k,k+2) for k in range(n+1)] for n in range(16)]) # _G. C. Greubel_, Jan 10 2023
%Y A106262 Cf. A106263 (row sums), A106264 (diagonal sums).
%Y A106262 Cf. A000034, A015910, A062173, A112983, A213859, A294389, A294390.
%K A106262 easy,nonn,tabl
%O A106262 0,5
%A A106262 _Paul Barry_, Apr 28 2005