cp's OEIS Frontend

A319391 a(n) = (1 + 2)^3 + (4 + 5)^6 + (7 + 8)^9 + (10 + 11)^12 + ... + (up to n).

%I A319391 #12 Oct 05 2018 18:46:45
%S A319391 1,3,27,31,36,531468,531475,531483,38443890843,38443890853,
%T A319391 38443890864,7355865955277484,7355865955277497,7355865955277511,
%U A319391 2954320062416788976127,2954320062416788976143,2954320062416788976160,2154028838712789034859190336
%N A319391 a(n) = (1 + 2)^3 + (4 + 5)^6 + (7 + 8)^9 + (10 + 11)^12 + ... + (up to n).
%H A319391 Robert Israel, <a href="/A319391/b319391.txt">Table of n, a(n) for n = 1..353</a>
%F A319391 a(n) = Sum_{i=1..n} (floor(i/3)-floor((i-1)/3))*(6*floor((i+2)/3)-3)^(3*floor((i+2)/3)) + i*(floor((i-1)/3)-floor((i-2)/3))+i*(floor((i+1)/3)-floor(i/3))-(6*floor((i+2)/3)-3)*(floor(i/3)-floor((i-1)/3)).
%F A319391 If 3|n then a(n) = a(n-3)+(2*n-3)^n, otherwise a(n) = a(n-1)+n. - _Robert Israel_, Oct 05 2018
%e A319391 a(1) = 1;
%e A319391 a(2) = 1 + 2 = 3;
%e A319391 a(3) = (1 + 2)^3 = 27;
%e A319391 a(4) = (1 + 2)^3 + 4 = 31;
%e A319391 a(5) = (1 + 2)^3 + 4 + 5 = 36;
%e A319391 a(6) = (1 + 2)^3 + (4 + 5)^6 = 531468;
%e A319391 a(7) = (1 + 2)^3 + (4 + 5)^6 + 7 = 531475;
%e A319391 a(8) = (1 + 2)^3 + (4 + 5)^6 + 7 + 8 = 531483;
%e A319391 a(9) = (1 + 2)^3 + (4 + 5)^6 + (7 + 8)^9 = 38443890843;
%e A319391 a(10) = (1 + 2)^3 + (4 + 5)^6 + (7 + 8)^9 + 10 = 38443890853; etc.
%p A319391 f:= proc(n) option remember;
%p A319391   if n mod 3 = 0 then procname(n-3)+(2*n-3)^n
%p A319391   else procname(n-1)+n
%p A319391   fi
%p A319391 end proc:
%p A319391 f(0):= 0:
%p A319391 map(f, [$1..20]); # _Robert Israel_, Oct 05 2018
%t A319391 Table[Sum[(Floor[i/3] - Floor[(i - 1)/3])*(6*Floor[(i + 2)/3] - 3)^(3*Floor[(i + 2)/3]) + i*(Floor[(i - 1)/3] - Floor[(i - 2)/3]) + i*(Floor[(i + 1)/3] - Floor[i/3]) - (6*Floor[(i + 2)/3] - 3)*(Floor[i/3] - Floor[(i - 1)/3]), {i, n}], {n, 20}]
%Y A319391 Cf. A305189, A318868, A319014, A319258.
%K A319391 nonn,easy
%O A319391 1,2
%A A319391 _Wesley Ivan Hurt_, Sep 18 2018