A260307 a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-6) - a(n-7) - a(n-8) + a(n-9) with a(0) - a(8) as shown below.

1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 13, 10, 15, 12, 17, 14, 20, 15, 22, 17, 24, 19, 27, 20, 29, 22, 31, 24, 34, 25, 36, 27, 38, 29, 41, 30, 43, 32, 45, 34, 48, 35, 50, 37, 52, 39, 55, 40, 57, 42, 59, 44, 62, 45, 64, 47, 66, 49, 69, 50, 71, 52, 73, 54, 76, 55, 78

Offset

0,2

Comments

A260708 difference table rows have the same nine-step recurrence:

0, 1, 3, 6, 10, 16, 21, 29, 36, 46, 55, 65, 78, 93, ...

1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 13, 10, 15, 12, ... = a(n)

1, 1, 1, 2, -1, 3, -1, 3, -1, 4, -3, 5, -3, 5, ... = b(n)

0, 0, 1, -3, 4, -4, 4, -4, 5, -7, 8, -8, 8, -8, ... (see A042965(n)).

(b(2n) + b(2n+1) = A052901(n+2).)

Links

G. C. Greubel, Table of n, a(n) for n = 0..1500

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

Formula

a(2n) = A047282(n). a(2n+1) = A047212(n+1).

a(n) = A260708(n+1) - A260708(n).

a(n+6) = a(n) + period of length 2: repeat 7, 5.

a(2n) + a(2n+1) = 3 + 4*n.

a(n) = n + 1 + (-1)^n*A152467(n+2).

From Colin Barker, Nov 22 2015: (Start)

a(n) = a(n-2) + a(n-6) - a(n-8) for n>7.

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

(End)

Mathematica

RecurrenceTable[{a[n] == a[n-2] + a[n-6] - a[n-8], a[0]=1, a[1]=2, a[2]=3, a[3]=4, a[4]=6, a[5]=5, a[6]=8, a[7]=7}, a, {n, 0, 100}] (* G. C. Greubel, Nov 23 2015 *)

Prog

(PARI) Vec((x^6+x^5+3*x^4+2*x^3+2*x^2+2*x+1)/((x-1)^2*(x+1)^2*(x^2-x+1)*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Nov 22 2015
(PARI) vector(100, n, n--; n + (-1)^n *((n+2)\6) + 1) \\ Altug Alkan, Nov 24 2015
(Magma) I:=[1, 2, 3, 4, 6, 5, 8, 7]; [n le 8 select I[n] else Self(n-2) + Self(n-6) - Self(n-8): n in [1..70]]; // Vincenzo Librandi, Dec 26 2015

Crossrefs

Cf. A004767, A010718, A042965, A047212, A047282, A052901, A152467, A260160 (eight-step recurrence), A260699 (nine-step recurrence), A260708.

Sequence in context: A121878 A167905 A285039 * A285041 A265734 A299759

Adjacent sequences: A260304 A260305 A260306 * A260308 A260309 A260310

Keyword

nonn,easy

Author

Paul Curtz, Nov 22 2015

Status

approved