OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 256.
LINKS
Colin Barker, Table of n, a(n) for n = 0..650
Henry Ernest Dudeney, Amusements in Mathematics, 1917. See problem 114, "Curious numbers".
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
a(0)=0, a(1)=48, a(2)=1680, a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3). - Harvey P. Dale, May 24 2014
From Colin Barker, Mar 02 2016: (Start)
a(n) = (-6+(3-2*sqrt(2))*(17+12*sqrt(2))^(-n)+(3+2*sqrt(2))*(17+12*sqrt(2))^n)/4.
G.f.: 48*x / ((1-x)*(1-34*x+x^2)).
(End)
a(n) = 34*a(n-1) - a(n-2) + 48. - Vincenzo Librandi, Mar 03 2016
EXAMPLE
48+1 = 49 = 7^2 and 48/2+1 = 24+1 = 25 = 5^2.
MAPLE
seq(coeff(series(48*x/((1-x)*(1-34*x+x^2)), x, n+1), x, n), n = 0..20); # G. C. Greubel, Sep 13 2019
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {0, 48, 1680}, 20] (* Harvey P. Dale, May 24 2014 *)
PROG
(PARI) concat(0, Vec(48*x/((1-x)*(1-34*x+x^2)) + O(x^20))) \\ Colin Barker, Mar 02 2016
(Magma) I:=[0, 48]; [n le 2 select I[n] else 34*Self(n-1) - Self(n-2)+48: n in [1..20]]; // Vincenzo Librandi, Mar 03 2016
(Sage)
def A008845_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P(48*x/((1-x)*(1-34*x+x^2))).list()
A008845_list(20) # G. C. Greubel, Sep 13 2019
(GAP) a:=[0, 48, 1680];; for n in [4..20] do a[n]:=35*a[n-1]-35*a[n-2] +a[n-3]; od; a; # G. C. Greubel, Sep 13 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved