A280167 a(2*n) = 3*n if n>0, a(2*n + 1) = -(2*n + 1), a(0) = 1.

1, -1, 3, -3, 6, -5, 9, -7, 12, -9, 15, -11, 18, -13, 21, -15, 24, -17, 27, -19, 30, -21, 33, -23, 36, -25, 39, -27, 42, -29, 45, -31, 48, -33, 51, -35, 54, -37, 57, -39, 60, -41, 63, -43, 66, -45, 69, -47, 72, -49, 75, -51, 78, -53, 81, -55, 84, -57, 87, -59

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

b(n) = -a(n) for n > 0 is multiplicative with b(2^e) = -3 * 2^(e-1) if e > 0, b(p^e) = p^e for prime p > 2.

Euler transform of length 10 sequence [-1, 3, 0, 0, 1, 0, 0, 0, 0, -1].

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

G.f.: (1 - x) * (1 - x^10) / ((1 - x^2)^3 * (1 - x^5)).

a(n) = (-1)^n * A257143(n). a(n) = (-1)^n * A080512(n) if n>0.

a(n) + a(n+1) = A084964(n-1) if n>0.

Example

G.f. = 1 - x + 3*x^2 - 3*x^3 + 6*x^4 - 5*x^5 + 9*x^6 - 7*x^7 + 12*x^8 + ...

Mathematica

a[ n_] := Which[ n < 1, Boole[n == 0], OddQ[n], -n, True, 3 n/2];
a[ n_] := SeriesCoefficient[ (1 - x + x^2 - x^3 + x^4) / (1 - 2*x^2 + x^4), {x, 0, n}];
Join[{1}, LinearRecurrence[{0, 2, 0, -1}, {-1, 3, -3, 6}, 50]] (* G. C. Greubel, Aug 01 2018 *)

Prog

(PARI) {a(n) = if( n<1, n==0, n%2, -n, 3*n/2)};
(PARI) {a(n) = if( n<0, 0, polcoeff( (1 - x) * (1 - x^10) / ((1 - x^2)^3 * (1 - x^5)) + x * O(x^n), n))};
(Magma) I:=[-1, 3, -3, 6]; [1] cat [n le 4 select I[n] else 2*Self(n-2) - Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 01 2018

Crossrefs

Cf. A080512, A084964, A257143.

Sequence in context: A265008 A165606 A295220 * A257143 A080512 A225441

Adjacent sequences: A280164 A280165 A280166 * A280168 A280169 A280170

Keyword

sign,easy

Author

Michael Somos, Dec 27 2016

Status

approved