%I A099964
%S A099964 1,1,1,1,2,2,3,3,3,6,8,8,14,17,17,31,39,39,39,78,109,126,126,235,313,
%T A099964 352,352,665,900,1026,1026,1926,2591,2943,2943,2943,5886,8477,10403,
%U A099964 11429,11429,21832,30309,36195,39138,39138,75333,105642,127474,138903
%N A099964 Triangle read by rows: The n-th row is constructed by forming the partial 
               sums of the previous row, reading from the right and if n is a triangular 
               number repeating the final term.
%C A099964 ...
%e A099964 Triangle begins
%e A099964 1
%e A099964 1 1
%e A099964 1 2
%e A099964 2 3 3
%e A099964 3 6 8
%e A099964 8 14 17
%e A099964 17 31 39 39
%e A099964 39 78 109 126
%e A099964 126 235 313 352
%e A099964 352 665 900 1026
%e A099964 1026 1926 2591 2943 2943
%p A099964 with(linalg):rev:=proc(a) local n, p; n:=vectdim(a): p:=i->a[n+1-i]: 
               vector(n,p) end: ps:=proc(a) local n, q; n:=vectdim(a): q:=i->sum(a[j],
               j=1..i): vector(n,q) end: pss:=proc(a) local n, q; n:=vectdim(a): 
               q:=proc(i) if i<=n then sum(a[j],j=1..i) else sum(a[j],j=1..n) fi 
               end: vector(n+1,q) end: tr:={seq(n*(n+1)/2,n=1..30)}: R[0]:=vector(1,
               1): for n from 1 to 15 do if member(n,tr)=false then R[n]:=ps(rev(R[n-1])) 
               else R[n]:=pss(rev(R[n-1])) fi od: for n from 0 to 15 do evalm(R[n]) 
               od; # (Deutsch)
%Y A099964 First column (and row sums) gives A099965. Cf. A099966, A099968.
%Y A099964 If an extra term is added to /every/ row we get A008282. Cf. A099959, 
               A099961.
%Y A099964 Sequence in context: A115733 A025496 A099959 this_sequence A094440 A093736 
               A076938
%Y A099964 Adjacent sequences: A099961 A099962 A099963 this_sequence A099965 A099966 
               A099967
%K A099964 nonn,tabf,nice,easy
%O A099964 0,5
%A A099964 N. J. A. Sloane (njas(AT)research.att.com), Nov 13 2004, following a 
               suggestion made by Douglas G. Rogers, Mar 10, 2003
%E A099964 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2004