A318868 -id:A318868 - cp's OEIS frontend

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

1, 3, 27, 31, 36, 531468, 531475, 531483, 38443890843, 38443890853, 38443890864, 7355865955277484, 7355865955277497, 7355865955277511, 2954320062416788976127, 2954320062416788976143, 2954320062416788976160, 2154028838712789034859190336

Offset: 1

Wesley Ivan Hurt, Sep 18 2018

			a(1) = 1;
a(2) = 1 + 2 = 3;
a(3) = (1 + 2)^3 = 27;
a(4) = (1 + 2)^3 + 4 = 31;
a(5) = (1 + 2)^3 + 4 + 5 = 36;
a(6) = (1 + 2)^3 + (4 + 5)^6 = 531468;
a(7) = (1 + 2)^3 + (4 + 5)^6 + 7 = 531475;
a(8) = (1 + 2)^3 + (4 + 5)^6 + 7 + 8 = 531483;
a(9) = (1 + 2)^3 + (4 + 5)^6 + (7 + 8)^9 = 38443890843;
a(10) = (1 + 2)^3 + (4 + 5)^6 + (7 + 8)^9 + 10 = 38443890853; etc.

Robert Israel, Table of n, a(n) for n = 1..353

Cf. A305189, A318868, A319014, A319258.

f:= proc(n) option remember;
  if n mod 3 = 0 then procname(n-3)+(2*n-3)^n
  else procname(n-1)+n
  fi
end proc:
f(0):= 0:
map(f, [$1..20]); # Robert Israel, Oct 05 2018

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}]

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)).

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

A319438 a(n) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11^12 + 13^14 - ... + (up to n).

Original entry on oeis.org

1, 1, -2, -80, -75, 15545, 15538, -5749256, -5749247, 3481035145, 3481035134, -3134947341576, -3134947341563, 3934241438357713, 3934241438357698, -6564474114274532912, -6564474114274532895, 14056519977953450458097, 14056519977953450458078

Offset: 1

Wesley Ivan Hurt, Sep 18 2018

An alternating version of A318868.

			   a(1) = 1;
   a(2) = 1^2 = 1;
   a(3) = 1^2 - 3 = -2;
   a(4) = 1^2 - 3^4 = -80;
   a(5) = 1^2 - 3^4 + 5 = -75;
   a(6) = 1^2 - 3^4 + 5^6 = 15545;
   a(7) = 1^2 - 3^4 + 5^6 - 7 = 15538;
   a(8) = 1^2 - 3^4 + 5^6 - 7^8 = -5749256;
   a(9) = 1^2 - 3^4 + 5^6 - 7^8 + 9 = -5749247;
  a(10) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 = 3481035145;
  a(11) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11 = 3481035134;
  a(12) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11^12 = -3134947341576; etc .

Colin Barker, Table of n, a(n) for n = 1..350

Cf. A093361, A228958, A305189, A318868.

Table[n*Mod[n, 2]*(-1)^(Floor[n/2]) + Sum[(2*i - 1)^(2*i)*(-1)^(i - 1), {i, Floor[n/2]}], {n, 30}]

a(n) = n*(n mod 2)*(-1)^floor(n/2) + Sum_{i=1..floor(n/2)} (2*i - 1)^(2*i)*(-1)^(i - 1).

cp's OEIS Frontend

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

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