cp's OEIS Frontend

A109433 Triangle read by rows: T(n,m) = number of binary numbers n+1 digits long which have m 1's as a substring.

%I A109433 #4 Mar 30 2012 17:31:16
%S A109433 1,2,1,4,2,1,8,5,2,1,16,11,5,2,1,32,24,12,5,2,1,64,51,27,12,5,2,1,128,
%T A109433 107,60,28,12,5,2,1,256,222,131,63,28,12,5,2,1,512,457,282,140,64,28,
%U A109433 12,5,2,1,1024,935,601,307,143,64,28,12,5,2,1,2048,1904,1270,666,316,144
%N A109433 Triangle read by rows: T(n,m) = number of binary numbers n+1 digits long which have m 1's as a substring.
%e A109433 T(4,2)=11 because of the sixteen binary digits which are 5 long, {10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111}, 11 have "11" as a substring.
%e A109433 Triangle begins:
%e A109433 n\m
%e A109433 0 1 0 0 0 0 0 0 0 0 0
%e A109433 1 2 1 0 0 0 0 0 0 0 0
%e A109433 2 4 2 1 0 0 0 0 0 0 0
%e A109433 3 8 5 2 1 0 0 0 0 0 0
%e A109433 4 16 11 5 2 1 0 0 0 0 0
%e A109433 5 32 24 12 5 2 1 0 0 0 0
%t A109433 T[n_, m_] := Length[ Select[ StringPosition[ #, ToString[(10^m - 1)/9]] & /@ Table[ ToString[ FromDigits[ IntegerDigits[i, 2]]], {i, 2^n, 2^(n + 1) - 1}], # != {} &]]; Flatten[ Table[ T[n, m], {n, 0, 11}, {m, n + 1}]]
%Y A109433 First column = A000079 = Powers of 2, the second column = A027934 = number of compositions of n with at least one even part and the last column = A045623 = number of 1's in all compositions of n+1.
%Y A109433 Cf. A000079, A027934, A045623, A109434, A109435.
%K A109433 base,nonn,tabl
%O A109433 0,2
%A A109433 _Robert G. Wilson v_, Jun 27 2005