cp's OEIS Frontend

A348647 Irregular table read by rows; the n-th row contains the lengths of the runs of consecutive terms with the same parity in the n-th row of Pascal's triangle (A007318).

%I A348647 #8 Oct 27 2021 15:26:08
%S A348647 1,2,1,1,1,4,1,3,1,2,2,2,1,1,1,1,1,1,1,8,1,7,1,2,6,2,1,1,1,5,1,1,1,4,
%T A348647 4,4,1,3,1,3,1,3,1,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,16,1,
%U A348647 15,1,2,14,2,1,1,1,13,1,1,1,4,12,4,1,3,1,11,1,3,1
%N A348647 Irregular table read by rows; the n-th row contains the lengths of the runs of consecutive terms with the same parity in the n-th row of Pascal's triangle (A007318).
%C A348647 For any n >= 0, the n-th row:
%C A348647 - is palindromic,
%C A348647 - has A038573(n+1) terms,
%C A348647 - has leading term A006519(n+1),
%C A348647 - has central term A080079(n+1).
%H A348647 Rémy Sigrist, <a href="/A348647/b348647.txt">Table of n, a(n) for n = 0..6304</a> (rows for n = 0..254, flattened)
%H A348647 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A348647 Sum_{k = 1..A038573(n+1)} T(n, k) = n+1.
%F A348647 T(n, 1) = A006519(n+1).
%F A348647 T(n, A048896(n)) = A080079(n+1).
%F A348647 T(2^k-1, 1) = 2^k for any k >= 0.
%e A348647 Triangle begins:
%e A348647     1;
%e A348647     2;
%e A348647     1, 1, 1;
%e A348647     4;
%e A348647     1, 3, 1;
%e A348647     2, 2, 2;
%e A348647     1, 1, 1, 1, 1, 1, 1;
%e A348647     8;
%e A348647     1, 7, 1;
%e A348647     2, 6, 2;
%e A348647     1, 1, 1, 5, 1, 1, 1;
%e A348647     4, 4, 4;
%e A348647     1, 3, 1, 3, 1, 3, 1;
%e A348647     2, 2, 2, 2, 2, 2, 2;
%e A348647     1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1;
%e A348647     16;
%e A348647     ...
%o A348647 (PARI) row(n) = { my (b=binomial(n)%2, r=[], p=1, w=1); for (k=2, #b, if (p==b[k], w++, r=concat(r, w); p=b[k]; w=1)); concat(r, w) }
%Y A348647 Cf. A006519, A007318, A038573, A047999, A048896, A080079.
%K A348647 nonn,look,tabf
%O A348647 0,2
%A A348647 _Rémy Sigrist_, Oct 27 2021