OFFSET
1,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
R. Evans, H. Hollmann, C. Krattenthaler and Q. Xiang, Gauss sums, Jacobi sums, and p-ranks of cyclic difference sets, J. Combin. Theory Ser. A, 87.1 (1999), 74-119.
Ronald Evans, Henk Hollmann, Christian Krattenthaler, and Qing Xiang, Supplement to "Gauss Sums, Jacobi Sums and p-ranks ..."
Q. Xiang, On Balanced Binary Sequences with Two-Level Autocorrelation Functions, IEEE Trans. Inform. Theory 44 (1998), 3153-3156.
FORMULA
G.f.: (1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5).
a(n+1) = a(n) + a(n-1) + a(n-2) + a(n-3) - 1, n >= 5.
MAPLE
L := 1, 1, 3, 7, 13: for i from 6 to 140 do l := nops([ L ]): L := L, op(l, [ L ])+op(l-1, [ L ])+op(l-2, [ L ])+op(l-3, [ L ])-1: od: [ L ];
MATHEMATICA
Join[{1, 1, 3, 7}, Table[a[1]=3; a[2]=1; a[3]=3; a[4]=7; a[i]=a[i-1]+a[i-2] +a[i-3]+a[i-4] -1, {i, 5, 40}]]
CoefficientList[Series[(1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5), {x, 0, 40}], x] (* G. C. Greubel, Jul 10 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5)) \\ G. C. Greubel, Jul 10 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5) )); // G. C. Greubel, Jul 10 2019
(Sage) ((1-x+x^2+x^3-x^4-2*x^5)/(1-2*x+x^5)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 10 2019
(GAP) a:=[1, 3, 7, 13];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]+a[n-3] +a[n-4] -1; od; Concatenation([1], a); # G. C. Greubel, Jul 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Christian Krattenthaler (kratt(AT)ap.univie.ac.at)
STATUS
approved