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A038201 5-wave sequence. 9
1, 1, 1, 1, 1, 2, 3, 4, 5, 9, 12, 14, 15, 29, 41, 50, 55, 105, 146, 175, 190, 365, 511, 616, 671, 1287, 1798, 2163, 2353, 4516, 6314, 7601, 8272, 15873, 22187, 26703, 29056, 55759, 77946, 93819, 102091, 195910, 273856, 329615, 358671, 688286, 962142 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

This sequence is related to the hendecagon or 11-gon, see A120747.

Sequence of perfect distributions for a cascade merge with six tapes according to Knuth. - Michael Somos, Feb 07 2004

REFERENCES

D. E. Knuth, Art of Computer Programming, Vol. 3, Sect. 5.4.3, Eq. (1).

LINKS

Table of n, a(n) for n=0..46.

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, Hendecagon , Wolfram Mathworld.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 1).

FORMULA

a(n) = a(n-1)+a(n-2) if n=4*m+1, a(n) = a(n-1)+a(n-4) if n=4*m+2, a(n) = a(n-1)+a(n-6) if n=4*m+3 and a(n) = a(n-1)+a(n-8) if n=4*m.

G.f.: -(1+x+x^2+x^3-2*x^4-x^5+x^7-x^8-x^11+x^12)/(-1+3*x^4+3*x^8-4*x^12-x^16+x^20).

a(n) =  3*a(n-4)+3*a(n-8)-4*a(n-12)-a(n-16)+a(n-20).

a(n-1) = sequence(sequence(T(n,k), k=2..5), n>=2) with a(0)=1; T(n,k) = sum(T(n-1,k1), k1 = 6-k..5) with T(1,1) = T(1,2) = T(1,3) = T(1,4) = 0 and T(1,5) = 1; n>=1 and 1 <= k <= 5. [Steinbach]

EXAMPLE

The first few rows of the T(n,k) array are, n>=1, 1 <= k <=5:

0,   0,   0,   0,   1

1,   1,   1,   1,   1

1,   2,   3,   4,   5

5,   9,   12,  14,  15

15,  29,  41,  50,  55

55,  105, 146, 175, 190

190, 365, 511, 616, 671

G.f. = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 9*x^8 + 12*x^9 + ...

MAPLE

m:=5: nmax:=12: 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[{0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 2, 3, 4, 5, 9, 12, 14, 15, 29, 41, 50, 55, 105, 146, 175}, 50] (* Harvey P. Dale, Dec 13 2012 *)

PROG

(PARI) {a(n) = local(m); if( n<=0, n==0, m = (n-1)\4 * 4; sum(k=2*m - n, m, a(k)))};

CROSSREFS

Cf. A038196, A038197.

The a(4*n) lead to A006358; the T(n,k) lead to A069006, A038342 and A120747.

Sequence in context: A093305 A065817 A084542 * A033084 A076134 A239742

Adjacent sequences:  A038198 A038199 A038200 * A038202 A038203 A038204

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 December 12 07:58 EST 2018. Contains 318053 sequences. (Running on oeis4.)