A038196 3-wave sequence starting with 1, 1, 1.

1, 1, 1, 2, 3, 5, 6, 11, 14, 25, 31, 56, 70, 126, 157, 283, 353, 636, 793, 1429, 1782, 3211, 4004, 7215, 8997, 16212, 20216, 36428, 45425, 81853, 102069, 183922, 229347, 413269, 515338, 928607, 1157954, 2086561, 2601899, 4688460, 5846414

Offset

0,4

Comments

The 3-wave sequence with initial values a, b, c is formed by the following construction:

a.......a+b+c............3a+5b+6c...

..b...b+c...a+2b+2c..2a+4b+5c...

....c..........a+2b+3c...

References

J. Kappraff, Beyond Measure, World Scientific, Inc. 2002, p. 497.

Links

Table of n, a(n) for n=0..40.

F. v. Lamoen, Wave sequences

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

Formula

a(n) = a(n-1) + a(n-2) if n is odd,

a(n) = a(n-1) + a(n-4) if n is even.

Also: a(n) = 2*a(n-2) + a(n-4) - a(n-6).

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

Prog

(PARI) a(n)=if(n>-1, polcoeff((1+x-x^2)/(1-2*x^2-x^4+x^6)+x*O(x^n), n), if(n<-3, polcoeff((1-x-x^2)/(1-x^2-2*x^4+x^6)+O(x^(-3-n)), -4-n), 0))

Crossrefs

a(2n) forms A006356, a(2n+1) ("the middle row") forms A006054. Cf. A038197, A038201, A187070.

Sequence in context: A276107 A187068 A187070 * A039849 A039896 A367212

Adjacent sequences: A038193 A038194 A038195 * A038197 A038198 A038199

Keyword

easy,nonn,changed

Author

Floor van Lamoen

Extensions

Edited by Floor van Lamoen, Feb 05 2002

Status

approved