%I #12 Jan 22 2022 19:44:31
%S 1,3,6,13,24,50,92,191,354,736,1374,2860,5370,11182,21090,43909,83112,
%T 172958,328340,682862,1299528,2700820,5150688,10697070,20437756,
%U 42415272,81170004,168337168,322613196,668607412,1283037084,2657319103,5105342946,10567113352,20323851054
%N Cumulative sums of the first ceiling(n/2)+1 elements of rows 0 to n in Pascal's triangle.
%e The first ceiling(n/2)+1 elements from the first four rows of Pascal's are:
%e 1
%e 1 1
%e 1 2
%e 1 3 3
%e So a(0)=1, a(1)=a(0)+1+1=3, a(2)=a(1)+1+2=6, a(3)=a(2)+1+3+3=13.
%o (Python)
%o seq=[];prev=[];total=0
%o for n in range(30):
%o row=[1]
%o last=int(n/2)
%o for k in range(last):
%o row.append(prev[k]+prev[k+1])
%o if n%2==1:
%o row.append(row[-1])
%o prev=row
%o total+=sum(row)
%o seq.append(total)
%o print(seq)
%Y Cf. A007318, A116496 (for n>=2, first differences).
%K nonn,easy
%O 0,2
%A _J. Stauduhar_, Jan 18 2022