cp's OEIS Frontend

A128221 A128174 * A127701.

%I A128221 #23 Jul 23 2024 08:40:56
%S A128221 1,1,2,1,1,3,1,2,1,4,1,1,3,1,5,1,2,1,4,1,6,1,1,3,1,5,1,7,1,2,1,4,1,6,
%T A128221 1,8,1,1,3,1,5,1,7,1,9,1,2,1,4,1,6,1,8,1,10,1,1,3,1,5,1,7,1,9,1,11,1,
%U A128221 2,1,4,1,6,1,8,1,10,1,12,1,1,3,1,5,1,7,1,9,1,11,1,13
%N A128221 A128174 * A127701.
%C A128221 Row sums = A024206: (1, 3, 5, 8, 11, 15, 19, ...). A128222 = A127701 * A128174.
%C A128221 Table T(n,k) = n, if k is odd, 1 if k is even; n, k > 0, read by antidiagonals. -_Boris Putievskiy_, Jan 30 2013
%H A128221 Robert G. Wilson v, <a href="/A128221/b128221.txt">Table of n, a(n) for n = 1..1000</a>
%F A128221 A128174 * A127701 as infinite lower triangular matrices. By columns, k-th column = k, 1, k, ...; k=1,2,3,...
%F A128221 From _Boris Putievskiy_, Jan 30 2013: (Start)
%F A128221 As table T(n,k) = (1+(-1)^k)/2 - (-1+(-1)^k)*n/2.
%F A128221 As linear sequence a(n) = (1+(-1)^A004736(n))/2 - (-1+(-1)^A004736(n))*A002260(n)/2. a(n) = (1+(-1)^j)/2 - (-1+(-1)^j)*i/2,
%F A128221 where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). (End)
%e A128221 From _Boris Putievskiy_, Jan 30 2013: (Start)
%e A128221 The start of the sequence as a table:
%e A128221   1, 1, 1, 1, 1, 1, 1, ...
%e A128221   2, 1, 2, 1, 2, 1, 2, ...
%e A128221   3, 1, 3, 1, 3, 1, 3, ...
%e A128221   4, 1, 4, 1, 4, 1, 4, ...
%e A128221   5, 1, 5, 1, 5, 1, 5, ...
%e A128221   6, 1, 6, 1, 6, 1, 6, ...
%e A128221   7, 1, 7, 1, 7, 1, 7, ...
%e A128221   ...
%e A128221 (End)
%e A128221 First few rows of the triangle are:
%e A128221   1;
%e A128221   1, 2;
%e A128221   1, 1, 3;
%e A128221   1, 2, 1, 4;
%e A128221   1, 1, 3, 1, 5;
%e A128221   1, 2, 1, 4, 1, 6;
%e A128221   1, 1, 3, 1, 5, 1, 7;
%e A128221   ...
%t A128221 a128221[n_, k_] := If[EvenQ[n-k], k, 1]/;1<=k<=n
%t A128221 a128221[r_] := Table[a128221[n, k], {n, 1, r}, {k, 1, n}]
%t A128221 TableForm[a128221[7]] (* triangle *)
%t A128221 Flatten[a128221[10]] (* data *) (* _Hartmut F. W. Hoft_, Mar 08 2017 *)
%t A128221 t[r_, c_] := If[ OddQ@ c, r, 1]; Table[t[k, n - k + 1], {n, 13}, {k, n}] // Flatten (* _Robert G. Wilson v_, Mar 09 2017 *)
%Y A128221 Cf. A128174, A127701, A024206, A128222.
%K A128221 nonn,tabl
%O A128221 1,3
%A A128221 _Gary W. Adamson_, Feb 19 2007
%E A128221 More terms from _Robert G. Wilson v_, Mar 09 2017