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A064520 a(n) = + 1 - 2 - 3 + 4 + 5 + 6 - 7 - 8 - 9 - 10 + 11 + 12 + 13 + 14 + 15 - ... + (+-1)*n, where there is one plus, two minuses, three pluses, etc. (see A002024). 2
1, -1, -4, 0, 5, 11, 4, -4, -13, -23, -12, 0, 13, 27, 42, 26, 9, -9, -28, -48, -69, -47, -24, 0, 25, 51, 78, 106, 77, 47, 16, -16, -49, -83, -118, -154, -117, -79, -40, 0, 41, 83, 126, 170, 215, 169, 122, 74, 25, -25, -76, -128, -181, -235, -290, -234, -177, -119, -60, 0, 61, 123, 186, 250, 315, 381, 314, 246, 177 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

|a(n)| takes its locally maximal values when n is a triangular number, the maximal values being given by A019298.

The maximal positive/negative values occur for n = 1, 3, 6, 10, 15, 21 ... the triangular numbers and are a(n) = 1, -4, 11, -23, 42, -69,106, 215, 381, 616 ... +- int(sqrt(n^3/2) + 0.22098 * sqrt(n)). a(n) = n for n = 5, 13, 25, 41, 61, 85, ... m*(m*2-2)+1 and the previous number is equal to 0. Positive numbers which do not occur in this sequence are 2, 3, 6, 7, 8, 10, 12, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 43, 44, 45, 46, 48, ...

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = Sum_{k=1..n} (-1)^(A002024(k)+1)*k.

EXAMPLE

a(9) = -13 because 1 - 2 - 3 + 4 + 5 + 6 - 7 - 8 - 9 = -13.

MAPLE

a := proc(n) option remember: if n=1 then RETURN(1) fi: a(n-1) + n*(-1)^( floor(1/2 + sqrt(2*n)+1)); end: for n from 1 to 150 do printf(`%d, `, a(n)) od:

MATHEMATICA

Accumulate[Flatten[Table[(-1)^(n+1) Range[(n(n-1))/2+1, (n(n+1))/2], {n, 15}]]] (* Harvey P. Dale, Apr 22 2015 *)

PROG

(PARI) t(n) = floor(1/2+sqrt(2*n)) for(n=1, 200, print1(sum(k=1, n, (-1)^(t(k)+1)*k), " "))

(PARI) t(n)= { floor(sqrt(2*n) + 1/2) } { for (n=1, 1000, a=sum(k=1, n, (-1)^(t(k) + 1)*k); write("b064520.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 17 2009

CROSSREFS

Cf. A002024, A019298, A064528.

Sequence in context: A198747 A021965 A164108 * A267313 A108174 A134530

Adjacent sequences:  A064517 A064518 A064519 * A064521 A064522 A064523

KEYWORD

sign,look,easy

AUTHOR

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 07 2001

EXTENSIONS

More terms from James A. Sellers, Jason Earls and Vladeta Jovovic, Oct 08 2001

STATUS

approved

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Last modified May 23 11:20 EDT 2019. Contains 323514 sequences. (Running on oeis4.)