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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 17:18 EST 2019. Contains 329879 sequences. (Running on oeis4.)