OFFSET
1,2
REFERENCES
Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-1,1).
FORMULA
G.f.: x/(1 - 3*x + x^2 + x^3 - x^4).
a(n) ~ 0.50556... * 2.505068...^n. - Charles R Greathouse IV, Aug 06 2012
a(n) = 3*a(n-1) - a(n-2) - a(n-3) + a(n-4) for n>4. - Wesley Ivan Hurt, Sep 18 2015
EXAMPLE
x + 3*x^2 + 8*x^3 + 20*x^4 + 50*x^5 + 125*x^6 + 313*x^7 + 784*x^8 + 1964*x^9 + ...
MATHEMATICA
nn = 30; CoefficientList[Series[x/(1 - 3*x + x^2 + x^3 - x^4), {x, 0, nn}], x]
LinearRecurrence[{3, -1, -1, 1}, {1, 3, 8, 20}, 40] (* Harvey P. Dale, Nov 09 2020 *)
PROG
(PARI) a(n)=polcoeff(x/(1-3*x+x^2+x^3-x^4)+O(x^(n+1)), n) \\ Charles R Greathouse IV, Aug 06 2012
(Magma) I:=[1, 3, 8, 20]; [n le 4 select I[n] else 3*Self(n-1)-Self(n-2)-Self(n-3)+Self(n-4): n in [1..40]] // Vincenzo Librandi, Aug 07 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 19 2006
EXTENSIONS
Edited by N. J. A. Sloane, Sep 21 2006; definition corrected Aug 06 2012
STATUS
approved