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%I #21 May 12 2019 02:18:33
%S 0,1,0,2,2,1,3,4,3,0,4,6,5,3,1,5,8,7,6,4,2,6,10,9,9,7,5,0,7,12,11,12,
%T 10,8,4,1,8,14,13,15,13,11,8,5,2,9,16,15,18,16,14,12,9,6,3,10,18,17,
%U 21,19,17,16,13,10,7,0
%N T(n,k) = A002024(k+1)*n + A002262(k), n >= 0, k >= 0, read by antidiagonals.
%C A table of congruences.
%C See A182631 for another version.
%e Table of congruences:
%e ===============+====+=======+==========+=============+====
%e mod | 1 | 2 | 3 | 4 | ...
%e ===============+====+=======+==========+=============+====
%e congruent to | 0 | 0 1 | 0 1 2 | 0 1 2 3 | ...
%e ===============+====+=======+==========+=============+====
%e Array begins: | 0 | 0 1 | 0 1 2 | 0 1 2 3 | ...
%e | 1 | 2 3 | 3 4 5 | 4 5 6 7 | ...
%e | 2 | 4 5 | 6 7 8 | 8 9 10 11 | ...
%e | 3 | 6 7 | 9 10 11 | 12 13 14 15 | ...
%e | 4 | 8 9 | 12 13 14 | 16 17 18 19 | ...
%e | 5 | 10 11 | 15 16 17 | 20 21 22 23 | ...
%e | 6 | 12 13 | 18 19 20 | 24 25 26 27 | ...
%e | 7 | 14 15 | 21 22 23 | 28 29 30 31 | ...
%e | 8 | 16 17 | 24 25 26 | 32 33 34 35 | ...
%e | 9 | 18 19 | 27 28 29 | 36 37 38 39 | ...
%e | 10 | 20 21 | 30 31 32 | 40 41 42 43 | ...
%p A002262 := proc(n) n-binomial(floor(1/2+sqrt(2+2*n)),2) ; end proc:
%p A002024 := proc(n) ceil((sqrt(1+8*n)-1)/2) ;end proc:
%p A182630 := proc(n,k) A002024(k+1)*n+A002262(k) ; end proc: # _R. J. Mathar_, Dec 09 2010
%Y Columns: A001477, A005483, A005408, A008585, A016777, A016789, A008586, A016813, A016825, A004767.
%Y Rows: A002262, A094727, A182815.
%Y Cf. A182631.
%K nonn,tabl,easy
%O 0,4
%A _Omar E. Pol_, Dec 06 2010
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