cp's OEIS Frontend

A182630 T(n,k) = A002024(k+1)*n + A002262(k), n >= 0, k >= 0, read by antidiagonals.

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