cp's OEIS Frontend

A103452 Inverse of number triangle A103451.

%I A103452 #29 Jun 18 2021 02:38:50
%S A103452 1,-1,1,-1,0,1,-1,0,0,1,-1,0,0,0,1,-1,0,0,0,0,1,-1,0,0,0,0,0,1,-1,0,0,
%T A103452 0,0,0,0,1,-1,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,
%U A103452 0,1,-1,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,1
%N A103452 Inverse of number triangle A103451.
%C A103452 Triangle T(n,k), 0 <= k <= n, read by rows given by [ -1, 2, 0, 0, 0, 0, 0, ...] DELTA [1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, May 01 2007
%H A103452 Michael De Vlieger, <a href="/A103452/b103452.txt">Table of n, a(n) for n = 0..10010</a> (Rows 0 <= n <= 140)
%F A103452 T(n,k) = 1 if k = n, -1 if k = 0, otherwise 0.
%F A103452 Sum_{k=0..n} T(n, k) = 0^n (row sums).
%F A103452 Sum_{k=0..floor(n/2)} T(n-k, k) = 0^n - (1-(-1)^n)/2 (diagonal sums).
%F A103452 G.f.: (1 - 2*x + y*x^2)/((1-x)*(1-y*x)). - _Philippe Deléham_, Feb 11 2012
%e A103452 Triangle begins
%e A103452    1;
%e A103452   -1, 1;
%e A103452   -1, 0, 1;
%e A103452   -1, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 0, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 0, 0, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A103452   -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%e A103452 Production matrix begins
%e A103452   -1, 1;
%e A103452   -2, 1, 1;
%e A103452   -2, 1, 0, 1;
%e A103452   -2, 1, 0, 0, 1;
%e A103452   -2, 1, 0, 0, 0, 1;
%e A103452   -2, 1, 0, 0, 0, 0, 1;
%e A103452   -2, 1, 0, 0, 0, 0, 0, 1;
%e A103452   -2, 1, 0, 0, 0, 0, 0, 0, 1;
%t A103452 Table[Range[n] /. {k_ /; k == 1 && n != 1 -> -1, k_ /; k == n -> 1, _Integer -> 0}, {n, 15}] // Flatten (* _Michael De Vlieger_, Jul 21 2016 *)
%o A103452 (Sage) flatten([[1 if k==n else -1 if k==0 else 0 for k in (0..n)] for n in (0..15)]) # _G. C. Greubel_, Jun 18 2021
%Y A103452 Cf. A000007 (row sums), A103453, A103454, A103455.
%K A103452 easy,sign,tabl
%O A103452 0,1
%A A103452 _Paul Barry_, Feb 06 2005