A061883 Largest triangular number less than or equal to sum of previous terms with a(0)=1.

1, 1, 1, 3, 6, 10, 21, 36, 78, 153, 300, 595, 1176, 2346, 4656, 9316, 18528, 37128, 74305, 148240, 296835, 593505, 1186570, 2372931, 4744740, 9489546, 18975880, 37953828, 75909681, 151806600, 303626403, 607243825, 1214480970, 2428940451

Offset: 0

Author

Henry Bottomley, May 12 2001

Keywords

• nonn

Comments

a(5)=10 since 1+1+1+3+6=12 and 10 is the largest triangular number less than or equal to this.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Programs

Haskell

a061883 n = a061883_list !! n
a061883_list = 1 : zipWith (-) (tail a060985_list) a060985_list
-- Reinhard Zumkeller, Feb 03 2012

Mathematica

ltn[n_]:=Module[{c=Floor[(Sqrt[8*n+1]-1)/2]},(c(c+1))/2]; nxt[{t_, a_}] := Module[ {m = ltn[t]}, {t + m, m}]; Transpose[NestList[nxt,{1,1},40]] [[2]] (* Harvey P. Dale, Feb 12 2016 *)

Formula

a(n) = A060985(n+1)-A060985(n) = A057944(A060985(n)) = A000217(A003056(A060985(n)))