Search: id:A099959
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%I A099959
%S A099959 1,1,1,1,1,2,2,3,3,3,6,8,8,14,17,17,17,34,48,56,56,104,138,155,155,155,
%T A099959 310,448,552,608,608,1160,1608,1918,2073,2073,2073,4146,6064,7672,8832,
%U A099959 9440,9440,18272,25944,32008,36154,38227,38227,38227,76454,112608
%N A099959 Triangle read by rows: Each row is constructed by forming the partial 
               sums of the previous row, reading from the right and at every other 
               row repeating the final term.
%C A099959 ...
%e A099959 Triangle begins
%e A099959 1
%e A099959 1
%e A099959 1 1
%e A099959 1 2
%e A099959 2 3 3
%e A099959 3 6 8
%e A099959 8 14 17 17
%e A099959 17 34 48 56
%e A099959 56 104 138 155 155
%p A099959 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: R[0]:=vector(1,1): for n from 1 to 18 do 
               if n mod 2 = 1 then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) 
               fi od: for n from 0 to 18 do evalm(R[n]) od; # program yields the 
               successive rows (Deutsch)
%Y A099959 First column (and row sums) gives A099960.
%Y A099959 If an extra term is added to /every/ row we get A008282. Cf. A099961.
%Y A099959 Sequence in context: A080968 A115733 A025496 this_sequence A099964 A094440 
               A093736
%Y A099959 Adjacent sequences: A099956 A099957 A099958 this_sequence A099960 A099961 
               A099962
%K A099959 nonn,tabf,nice,easy
%O A099959 0,6
%A A099959 N. J. A. Sloane (njas(AT)research.att.com), Nov 13 2004, following a 
               suggestion made by Douglas G. Rogers, Mar 10, 2003
%E A099959 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 16 2004

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