A099962 First column (also row sums) of triangle in A099961.

1, 1, 1, 1, 2, 3, 5, 13, 28, 64, 207, 578, 1685, 6518, 22361, 79319, 357180, 1453177, 6075215, 31216968, 146906126, 707344776, 4084254624, 21823224623, 118932148555, 762346849634, 4559139897594, 27742486678915, 195472113041924

Offset: 0

Author

N. J. A. Sloane, Nov 13 2004

Keywords

• nonn
• easy

Crossrefs

Cf. A099961.

Programs

Maple

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 35 do if n mod 3 = 0 or n mod 3 = 1 then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: seq(R[n][1],n=0..35); # Emeric Deutsch, Nov 16 2004

Mathematica

r[n_] := r[n] = If[n == 0, {1}, Module[{a}, Join[a = Accumulate[Reverse[r[n-1]]], If[Mod[n, 3] == 2, {Last[a]}, {}]]]];
a[n_] := If[n == 0, 1, r[n][[1]]];
Table[a[n], {n, 0, 28}] (* Jean-François Alcover, Mar 10 2023 *)

Extensions

More terms from Emeric Deutsch, Nov 16 2004