A099966 Sequence of the next-to-last entries in the rows of A099964.

1, 1, 3, 6, 14, 39, 109, 313, 900, 2943, 10403, 36195, 127474, 447352, 1711141, 7234223, 29672119, 123515469, 511672779, 2123410053, 9349845765, 45883313142, 216991244323, 1041956760633, 4977352149113, 23819499579914

Offset: 1

Author

N. J. A. Sloane, Nov 13 2004

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..750

Crossrefs

Cf. A099964, A099965.

Programs

Haskell

a099966 n = a099966_list !! (n-1)
a099966_list = map (last . init) $ tail 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 30 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][vectdim(R[n])-1],n=1..30); # Emeric Deutsch, Nov 16 2004

Mathematica

triQ[n_] := Module[{k}, 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]); a[n_] := row[n][[-2]]; Array[a, 26] (* Jean-François Alcover, Feb 13 2018 *)

Extensions

More terms from Emeric Deutsch, Nov 16 2004

Offset corrected by Reinhard Zumkeller, May 02 2012