A099965 First column (also row sums) of triangle in A099964.

1, 1, 1, 2, 3, 8, 17, 39, 126, 352, 1026, 2943, 11429, 39138, 138903, 486490, 1711141, 7720713, 31383260, 131236182, 543056039, 2254646235, 9349845765, 48137959377, 226341090088, 1090094720010, 5203693239201, 24909594299924

Offset: 0

Author

N. J. A. Sloane, Nov 13 2004

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..750

Crossrefs

Cf. A099964.

Programs

Haskell

a099965 = flip a099964 0
a099965_list = map head a099964_tabf
-- Reinhard Zumkeller, May 02 2012

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: tr:={seq(n*(n+1)/2,n=1..30)}: R[0]:=vector(1,1): for n from 1 to 31 do if member(n,tr)=false then R[n]:=ps(rev(R[n-1])) else R[n]:=pss(rev(R[n-1])) fi od: seq(R[n][1],n=0..31); # Emeric Deutsch, Nov 16 2004

Mathematica

triQ[n_] := Reduce[n == k (k + 1)/2, k, Integers] =!= False; row[0] = {1}; row[1] = {1, 1}; row[n_] := row[n] = (ro = Accumulate[Reverse[row[n-1]]]; If[triQ[n], Append[ro, Last[ro]], ro]); Table[row[n][[1]], {n, 0, 27}] (* Jean-François Alcover, Feb 10 2018 *)

Extensions

More terms from Emeric Deutsch, Nov 16 2004