cp's OEIS Frontend

A360800 Numbers Sum_{i=1..2r+1} 2^k(i) such that k(1) is even and, for r > 0 and i < 2r+1, the difference k(i+1)-k(i) is > 0 and odd.

%I A360800 #9 Mar 31 2023 15:00:14
%S A360800 1,4,7,16,19,25,28,31,64,67,73,76,79,97,100,103,112,115,121,124,127,
%T A360800 256,259,265,268,271,289,292,295,304,307,313,316,319,385,388,391,400,
%U A360800 403,409,412,415,448,451,457,460,463,481,484,487,496,499,505,508,511,1024
%N A360800 Numbers Sum_{i=1..2r+1} 2^k(i) such that k(1) is even and, for r > 0 and i < 2r+1, the difference k(i+1)-k(i) is > 0 and odd.
%C A360800 This is a subsequence of A360799. Another description of the terms: in the base-2 representation, the number of ones is odd and all zeros are grouped in blocks of even length.
%C A360800 That is why the terms less than 2^(2j+1) describe start profiles for tiling a (2j+1) X m wall with 1 X 2 dominos, see examples and A360799.
%e A360800 A 5 X m wall is tiled bottom-up with dominos, start profiles:
%e A360800             _        _            _ _ _    _     _ _    _ _ _ _ _
%e A360800     ___ ___| |   ___| |___    ___| | | |  | |___| | |  | | | | | |
%e A360800    |___|___|_|  |___|_|___|  |___|_|_|_|  |_|___|_|_|  |_|_|_|_|_|
%e A360800     0 0 0 0 1    0 0 1 0 0    0 0 1 1 1    1 0 0 1 1    1 1 1 1 1
%e A360800     1 = a(1)     4 = a(2)     7 = a(3)     19 = a(5)    31 = a(7)
%e A360800     also the mirror images of 1 (16), 19 (25) and 7 (28).
%o A360800 (Maxima)
%o A360800 block(kmax: 100, a:[],
%o A360800  oddsum(y):= block(su1:0, su2:0, pold:0, ok: true,
%o A360800   while y>0 and ok do(p:mod(y,2), y:(y-p)/2,
%o A360800    if p=1 then(if pold=0 and su2=1 then ok:false, su1:1-su1, su2:0)
%o A360800    elseif p=0 then su2:1-su2, pold:p), return(is(ok and su1=1))),
%o A360800 for k from 1 thru kmax do if oddsum(k) then a:append(a,[k]),a);
%Y A360800 Cf. A001835, A003775, A028469, A028471, A180963, A187616, A360799.
%K A360800 nonn
%O A360800 1,2
%A A360800 _Gerhard Kirchner_, Feb 24 2023