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A038197 4-wave sequence. 12
1, 1, 1, 1, 2, 3, 4, 7, 9, 10, 19, 26, 30, 56, 75, 85, 160, 216, 246, 462, 622, 707, 1329, 1791, 2037, 3828, 5157, 5864, 11021, 14849, 16886, 31735, 42756, 48620, 91376, 123111, 139997, 263108, 354484, 403104, 757588, 1020696, 1160693, 2181389 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

This sequence is related to the nonagon or 9-gon.

LINKS

Table of n, a(n) for n=0..43.

F. v. Lamoen, Wave sequences

P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.

Eric W. Weisstein, Nonagon , Wolfram Mathworld.

Index entries for linear recurrences with constant coefficients, signature (1,-1,3,-3,3,0,0,0,-1,1,-1).

FORMULA

a(n) = a(n-1)+a(n-2) if n=3*m+1, a(n) = a(n-1)+a(n-4) if n=3*m+2, a(n) = a(n-1)+a(n-6) if n=3*m. Also: a(n) = 2*a(n-3)+3*a(n-6)-a(n-9)-a(n-12).

G.f.: -(-1-x-x^2+x^3-x^5+x^6)/(1-2*x^3-3*x^6+x^9+x^12)

a(n-1) = sequence(sequence(T(n,k), k=2..4), n>=2) with a(0)=1; T(n,k) = sum(T(n-1,k1), k1 = 5-k..4) with T(1,1) = T(1,2) = T(1,3) = 0 and T(1,4) = 1; n>=1 and 1 <= k <= 4. [Steinbach]

EXAMPLE

The first few rows of the T(n,k) array are, n>=1, 1 <= k <=4:

0,  0,   0,   1

1,  1,   1,   1

1,  2,   3,   4

4,  7,   9,   10

10, 19,  26,  30

30, 56,  75,  85

85, 160, 216, 246

MAPLE

m:=4: nmax:=15: for k from 1 to m-1 do T(1, k):=0 od: T(1, m):=1: for n from 2 to nmax do for k from 1 to m do T(n, k):= add(T(n-1, k1), k1=m-k+1..m) od: od: for n from 1 to nmax/2 do seq(T(n, k), k=1..m) od; a(0):=1: Tx:=1: for n from 2 to nmax do for k from 2 to m do a(Tx):= T(n, k): Tx:=Tx+1: od: od: seq(a(n), n=0..Tx-1); # Johannes W. Meijer, Aug 03 2011

MATHEMATICA

LinearRecurrence[{1, -1, 3, -3, 3, 0, 0, 0, -1, 1, -1}, {1, 1, 1, 1, 2, 3, 4, 7, 9, 10, 19}, 50] (* Harvey P. Dale, Oct 02 2015 *)

CROSSREFS

The a(3*n) lead to A006357; The T(n,k) lead to A076264 and A091024.

Cf. A038196, A038201.

Cf. A120747 (m = 5: hendecagon or 11-gon)

Sequence in context: A138576 A259483 A187503 * A187506 A348443 A023546

Adjacent sequences:  A038194 A038195 A038196 * A038198 A038199 A038200

KEYWORD

easy,nonn

AUTHOR

Floor van Lamoen

EXTENSIONS

Edited by Floor van Lamoen, Feb 05 2002

Edited and information added by Johannes W. Meijer, Aug 03 2011

STATUS

approved

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Last modified May 24 11:49 EDT 2022. Contains 354033 sequences. (Running on oeis4.)