cp's OEIS Frontend

A318868 a(n) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11^12 + 13^14 + ... + (up to n).

%I A318868 #24 Sep 18 2018 06:27:41
%S A318868 1,1,4,82,87,15707,15714,5780508,5780517,3492564909,3492564920,
%T A318868 3141920941630,3141920941643,3940518306640919,3940518306640934,
%U A318868 6572348874019531544,6572348874019531561,14069656800941744522553,14069656800941744522572,37604043114346899937878154
%N A318868 a(n) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11^12 + 13^14 + ... + (up to n).
%H A318868 Colin Barker, <a href="/A318868/b318868.txt">Table of n, a(n) for n = 1..350</a>
%F A318868 a(n) = (2*floor((n-1)/2) + 1)*(n mod 2) + Sum_{i=1..floor(n/2)} (2*i - 1)^(2*i).
%e A318868 a(1) = 1;
%e A318868 a(2) = 1^2 = 1;
%e A318868 a(3) = 1^2 + 3 = 4;
%e A318868 a(4) = 1^2 + 3^4 = 82;
%e A318868 a(5) = 1^2 + 3^4 + 5 = 87;
%e A318868 a(6) = 1^2 + 3^4 + 5^6 = 15707;
%e A318868 a(7) = 1^2 + 3^4 + 5^6 + 7 = 15714;
%e A318868 a(8) = 1^2 + 3^4 + 5^6 + 7^8 = 5780508;
%e A318868 a(9) = 1^2 + 3^4 + 5^6 + 7^8 + 9 = 5780517;
%e A318868 a(10) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 = 3492564909;
%e A318868 a(11) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11 = 3492564920;
%e A318868 a(12) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11^12 = 3141920941630, etc.
%t A318868 Table[(2*Floor[(n - 1)/2] + 1)*Mod[n, 2] + Sum[(2*i - 1)^(2*i), {i, Floor[n/2]}], {n, 25}]
%o A318868 (PARI) a(n) = (2*((n-1)\2) + 1)*(n % 2) + sum(i=1, n\2, (2*i - 1)^(2*i)); \\ _Michel Marcus_, Sep 18 2018
%Y A318868 Cf. A093361, A228958, A305189.
%K A318868 nonn,easy
%O A318868 1,3
%A A318868 _Wesley Ivan Hurt_, Sep 16 2018