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A318868 a(n) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11^12 + 13^14 + ... + (up to n). 3
1, 1, 4, 82, 87, 15707, 15714, 5780508, 5780517, 3492564909, 3492564920, 3141920941630, 3141920941643, 3940518306640919, 3940518306640934, 6572348874019531544, 6572348874019531561, 14069656800941744522553, 14069656800941744522572, 37604043114346899937878154 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

FORMULA

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

EXAMPLE

a(1) = 1;

a(2) = 1^2 = 1;

a(3) = 1^2 + 3 = 4;

a(4) = 1^2 + 3^4 = 82;

a(5) = 1^2 + 3^4 + 5 = 87;

a(6) = 1^2 + 3^4 + 5^6 = 15707;

a(7) = 1^2 + 3^4 + 5^6 + 7 = 15714;

a(8) = 1^2 + 3^4 + 5^6 + 7^8 = 5780508;

a(9) = 1^2 + 3^4 + 5^6 + 7^8 + 9 = 5780517;

a(10) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 = 3492564909;

a(11) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11 = 3492564920;

a(12) = 1^2 + 3^4 + 5^6 + 7^8 + 9^10 + 11^12 = 3141920941630, etc.

MATHEMATICA

Table[(2*Floor[(n - 1)/2] + 1)*Mod[n, 2] + Sum[(2*i - 1)^(2*i), {i, Floor[n/2]}], {n, 25}]

PROG

(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

CROSSREFS

Cf. A093361, A228958, A305189.

Sequence in context: A090599 A133396 A233001 * A289224 A158981 A317889

Adjacent sequences:  A318865 A318866 A318867 * A318869 A318870 A318871

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Sep 16 2018

STATUS

approved

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Last modified October 6 00:49 EDT 2022. Contains 357261 sequences. (Running on oeis4.)