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

0,4

Links

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

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 *)

Prog

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

Crossrefs

Cf. A099964.

Sequence in context: A256169 A298405 A219788 * A319566 A294450 A345243

Adjacent sequences: A099962 A099963 A099964 * A099966 A099967 A099968

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 13 2004

Extensions

More terms from Emeric Deutsch, Nov 16 2004

Status

approved