A309311 - OEIS

%I #18 Sep 01 2019 22:06:30

%S 1,2,3,6,12,18,42,60,144,264,510,1062,1572,2634,5778,12024,22008,

%T 45852,67860,159852,227712,387564,842988,1765860,3543828,7041516,

%U 13809468,27778788,55397724,104027496,211598820,426741468,849939108,1696334388,3385627260,6785383692

%N 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).

%C 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).

%H Robert Israel, <a href="/A309311/b309311.txt">Table of n, a(n) for n = 1..3550</a>

%e Calculating a(8):

%e 8=n+1, n=7

%e a(7)=42 so k=2

%e m=n+1-k=6

%e a(8)=Sum_{i=6..7} a(i)=a(6)+a(7)

%e a(8)=60

%p A[1]:= 1: S[0]:= 0: S[1]:= 1:

%p A[2]:= 2: S[2]:= 3:

%p for n from 2 to 99 do

%p   k:= A[n] mod 10;

%p   if k <= 1 or k > n then A[n+1]:= S[n] else A[n+1]:= S[n] - S[n-k] fi;

%p   S[n+1]:= S[n]+A[n+1]

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Sep 01 2019

%t 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 *)

%K nonn,base,easy

%O 1,2

%A _Eder Vanzei_, Jul 22 2019

%E More terms from _Amiram Eldar_, Jul 23 2019

%E Edited by _N. J. A. Sloane_, Aug 31 2019