This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140503 #8 Aug 11 2022 09:57:52
%S A140503 1,-1,2,3,-2,4,-5,6,-4,8,11,-10,12,-8,16,-21,22,-20,24,-16,32,43,-42,
%T A140503 44,-40,48,-32,64,-85,86,-84,88,-80,96,-64,128,171,-170,172,-168,176,
%U A140503 -160,192,-128,256,-341,342,-340,344,-336,352,-320,384,-256,512,683,-682,684,-680
%N A140503 Triangle T(d,n) read by rows, the n-th term of the d-th differences of the Jacobsthal sequence A001045.
%C A140503 If interpreted as a flat sequence a(j), we obtain a(j+1)-2a(j)= -3, 4, -1, -8, 8, -13, 16, -16, 16, -5, -32, 32, -32, 32, -53, 64, ... which is essentially the negative values of A096773 padded by groups of one, then two, then three etc. signed elements of A098354.
%F A140503 T(d,n)=T(d-1,n+1)-T(d-1,n). T(0,n)=A001045(n).
%F A140503 Row sums: sum_{n=0..d-1} T(d,n) = A002450([(d+1)/2]).
%F A140503 Row sums of absolute values: sum_{n=0..d-1} |T(d,n)| = A045883(d).
%F A140503 T(d,n) = (2^n - 2^d*(-1)^(d+n))/3, for d > n >= 0. - _Jianing Song_, Aug 11 2022
%e A140503 A001045 and its d times iterated differences are
%e A140503 .0,.1,.1,.3,.5,11,21,43,...
%e A140503 .1,.0,.2,.2,.6,10,22,... < d=1
%e A140503 -1,.2,.0,.4,.4,12,... < d=2
%e A140503 .3,-2,.4,.0,.8,.. < d=3
%e A140503 -5,.6,-4,.8,.0,...
%e A140503 The sequence contains the first d elements of the d-th row, those up to the diagonal (which contains zeros).
%o A140503 (PARI) T(d,n) = (2^n - 2^d*(-1)^(d+n))/3 \\ _Jianing Song_, Aug 11 2022
%Y A140503 Cf. A001045, A140944 (with an extra diagonal of 0's).
%K A140503 sign,tabl,easy
%O A140503 1,3
%A A140503 _Paul Curtz_, Jun 30 2008
%E A140503 Edited by _R. J. Mathar_, Jul 14 2008