A187601 n/2 times period 6 sequence [1, 2, 3, 4, 3, 2, ...].

0, 1, 3, 6, 6, 5, 3, 7, 12, 18, 15, 11, 6, 13, 21, 30, 24, 17, 9, 19, 30, 42, 33, 23, 12, 25, 39, 54, 42, 29, 15, 31, 48, 66, 51, 35, 18, 37, 57, 78, 60, 41, 21, 43, 66, 90, 69, 47, 24, 49, 75, 102, 78, 53, 27, 55, 84, 114, 87, 59, 30, 61, 93, 126, 96, 65, 33, 67, 102

Offset: 0

Author

Bruno Berselli, Mar 11 2011

Keywords

• nonn
• look
• easy

Comments

A007310 is a subsequence.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (2,-1,-2,4,-2,-1,2,-1).

Crossrefs

Cf. A186813.

Cf. A109044, A088439 (by Superseeker).

Programs

Magma

[(n/2)*[1, 2, 3, 4, 3, 2][n mod 6 + 1]: n in [0..68]]; /* Other: */ [n*(5-2*(-1)^Floor((n+1)/3)-(-1)^n)/4: n in [0..68]];

Mathematica

CoefficientList[Series[x (1 + x + x^2 - x^3 + x^4 + x^5 + x^6) / ((1 - x)^2 (1 + x)^2 (1 - x + x^2)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Aug 19 2013 *)
LinearRecurrence[{2,-1,-2,4,-2,-1,2,-1},{0,1,3,6,6,5,3,7},90] (* Harvey P. Dale, Aug 20 2017 *)

Formula

a(n) = (n/2)*A028356(n).

G.f.: x*(1+x+x^2-x^3+x^4+x^5+x^6)/((1-x)^2*(1+x)^2*(1-x+x^2)^2).

a(-n) = -a(n). a(n) = 2*a(n-1)-a(n-2)-2*a(n-3)+4*a(n-4)-2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8) for n>7.

a(n) = n*(5-2*(-1)^floor((n+1)/3)-(-1)^n)/4.