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A273465 Numbers generated by starting at 1 and adding twice and subtracting once following the sequence of positive integers. 2
1, 3, 6, 2, 7, 13, 6, 14, 23, 13, 24, 36, 23, 37, 52, 36, 53, 71, 52, 72, 93, 71, 94, 118, 93, 119, 146, 118, 147, 177, 146, 178, 211, 177, 212, 248, 211, 249, 288, 248, 289, 331, 288, 332, 377, 331, 378, 426, 377, 427 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is generated by listing the successive results of 1 + 2 + 3 - 4 + 5 + 6 - 7 + 8 + 9 - 10 + ... etc.

By adding twice and subtracting once, the results at positions i, i+2 and i+4 are linked by the relationship: n, n+1, n.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

FORMULA

Let the sequence be written 1, 3, a, 2, a+1, b, a, b+1, c, b, c+1, d, c, ... The (a, a+1, a) triple at positions i, i+2, i+4 can be determined from the previous two sequences: (c = 2*b - a + 3). This new sequence starts at position i+3.

G.f.: (-2*z^6 - z^4 + 6*z^3 - 3*z^2 - 2*z - 1)/((z - 1)^3*(z^2 + z + 1)^2).

a(3*n-2) = A143689(n-1).

From Franck Maminirina Ramaharo, Dec 27 2018: (Start)

a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7), n >= 8.

E.g.f.: (1/18)*(exp(3*x/2)*(32 + 6*x + 3*x^2) + (4 - 12*x)*cos(sqrt(3)*x/2) - 4*sqrt(3)*(1 + x)*sin(sqrt(3)*x/2))/exp(x/2). (End)

EXAMPLE

n1 = 0 + 1 = 1

n2 = 1 + 2 = 3

n3 = 1 + 2 + 3 = 6

n4 = 1 + 2 + 3 - 4 = 2

n5 = 1 + 2 + 3 - 4 + 5 = 7

n6 = 1 + 2 + 3 - 4 + 5 + 6 = 13

n7 = 1 + 2 + 3 - 4 + 5 + 6 - 7 = 6

...

->

(n3, n5, n7) = (6, 7, 6)

(n6, n8, n10) = (13, 14, 13)

...

->

n9 = 2.n6 - n7 + 3 = 23

MATHEMATICA

Accumulate@ Table[If[Mod[n, 3] == 1 && n > 1, -n, n], {n, 50}] (* Michael De Vlieger, May 23 2016 *)

CROSSREFS

Cf. A143689.

Sequence in context: A249558 A072007 A078783 * A328503 A333826 A125717

Adjacent sequences:  A273462 A273463 A273464 * A273466 A273467 A273468

KEYWORD

nonn

AUTHOR

Mattias Dooreman, May 23 2016

EXTENSIONS

a(25) corrected by Seiichi Manyama, May 26 2016

STATUS

approved

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Last modified May 18 12:53 EDT 2021. Contains 343995 sequences. (Running on oeis4.)