A097926 Number of (n,4) Freiman-Wyner sequences.

18, 36, 70, 134, 258, 498, 960, 1850, 3566, 6874, 13250, 25540, 49230, 94894, 182914, 352578, 679616, 1310002, 2525110, 4867306, 9382034, 18084452, 34858902, 67192694, 129518082, 249654130, 481223808, 927588714, 1787984734, 3446451386

Offset: 5

Author

N. J. A. Sloane, Sep 05 2004

Keywords

• nonn

Comments

"The values for n <= 4 are straightforward."

References

• I. F. Blake, The enumeration of certain run length sequences, Information and Control, 55 (1982), 222-237.

Links

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

Crossrefs

Cf. A006355, A097925.

Programs

Maple

A097926 := proc(nmax) local a,n,k; k := 4 ; a := [18,36,70,134,258] ; while nops(a) < nmax do n := nops(a)+k+1 ; a := [op(a),2*op(n-1-k,a)-op(n-2*k-1,a) ] ; od ; end: nmax := 30 ; a := A097926(nmax) ; for i from 1 to nmax do printf("%d,",op(i,a)) ; od: # R. J. Mathar, Oct 31 2006

Mathematica

LinearRecurrence[{1,1,1,1},{18,36,70,134},30] (* Harvey P. Dale, Jun 06 2022 *)

Formula

a(n) = 2a(n-1) - a(n-k-1), k=4, n >= 2k+2. - R. J. Mathar, Oct 31 2006

G.f.: -2*(5*x^3+8*x^2+9*x+9)*x^5/(x^4+x^3+x^2+x-1) = -10*x^4-6*x^3-2*x^2-2+(-2*x^3-2+2*x)/(x^4+x^3+x^2+x-1). - R. J. Mathar, Nov 18 2007

Extensions

Corrected and extended by R. J. Mathar, Oct 31 2006