A309311 a(1)=1, a(2)=2; thereafter a(n+1) = Sum_{i=m..n} a(i) where m = (n+1)-k and k is the last digit of a(n), except if k=0, k=1, or k>n then a(n+1) = Sum_{i=1..n} a(i).

1, 2, 3, 6, 12, 18, 42, 60, 144, 264, 510, 1062, 1572, 2634, 5778, 12024, 22008, 45852, 67860, 159852, 227712, 387564, 842988, 1765860, 3543828, 7041516, 13809468, 27778788, 55397724, 104027496, 211598820, 426741468, 849939108, 1696334388, 3385627260, 6785383692

Offset

1,2

Comments

Briefly, a(n+1) is the sum of the previous terms up to a number m which is defined by the last digit of a(n).

Links

Robert Israel, Table of n, a(n) for n = 1..3550

Example

Calculating a(8):
8=n+1, n=7
a(7)=42 so k=2
m=n+1-k=6
a(8)=Sum_{i=6..7} a(i)=a(6)+a(7)
a(8)=60

Maple

A[1]:= 1: S[0]:= 0: S[1]:= 1:
A[2]:= 2: S[2]:= 3:
for n from 2 to 99 do
  k:= A[n] mod 10;
  if k <= 1 or k > n then A[n+1]:= S[n] else A[n+1]:= S[n] - S[n-k] fi;
  S[n+1]:= S[n]+A[n+1]
od:
seq(A[i], i=1..100); # Robert Israel, Sep 01 2019

Mathematica

a[1] = 1; a[2] = 2; a[n_] := a[n] = Module[{k = Mod[a[n - 1], 10]}, m = If[k > n - 1 || k == 0, 1, n - k]; Sum[a[i], {i, m, n - 1}]]; Array[a, 36] (* Amiram Eldar, Jul 23 2019 *)

Crossrefs

Sequence in context: A093687 A000423 A007335 * A361693 A103070 A233422

Adjacent sequences: A309308 A309309 A309310 * A309312 A309313 A309314

Keyword

nonn,base,easy

Author

Eder Vanzei, Jul 22 2019

Extensions

More terms from Amiram Eldar, Jul 23 2019

Edited by N. J. A. Sloane, Aug 31 2019

Status

approved