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A319438 a(n) = 1^2 - 3^4 + 5^6 - 7^8 + 9^10 - 11^12 + 13^14 - ... + (up to n). 1
1, 1, -2, -80, -75, 15545, 15538, -5749256, -5749247, 3481035145, 3481035134, -3134947341576, -3134947341563, 3934241438357713, 3934241438357698, -6564474114274532912, -6564474114274532895, 14056519977953450458097, 14056519977953450458078 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

An alternating version of A318868.

LINKS

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

FORMULA

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

EXAMPLE

   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 .

MATHEMATICA

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

CROSSREFS

Cf. A093361, A228958, A305189, A318868.

Sequence in context: A265585 A060051 A100421 * A195000 A073499 A222826

Adjacent sequences:  A319435 A319436 A319437 * A319439 A319440 A319441

KEYWORD

sign,easy

AUTHOR

Wesley Ivan Hurt, Sep 18 2018

STATUS

approved

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Last modified November 29 08:19 EST 2020. Contains 338761 sequences. (Running on oeis4.)