OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 20, ..., in the square spiral whose vertices are the generalized dodecagonal numbers A195162. Semiaxis opposite to A195317 in the same spiral.
a(n) is the sum of all the integers less than 10*n which are not multiple of 2 or 5. a(2) = (1 + 3 + 7 + 9) + (11 + 13 + 17 + 19) = 20 + 60 = 80 = 20 * 2^2. (Link Crux Mathematicorum). - Bernard Schott, May 15 2017
Number of terms less than 10^k (k=0, 1, 2, ...): 1, 1, 3, 8, 23, 71, 224, 708, 2237, 7072, 22361, 70711, ... - Muniru A Asiru, Feb 01 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Léo Sauvé, Problem 53, Crux Mathematicorum, page 88, Vol.1, Nov. 75.
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(0)=0, a(1)=20, a(2)=80; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Jan 18 2013
EXAMPLE
From Muniru A Asiru, Feb 01 2018: (Start)
n=0, a(0) = 20*0^2 = 0.
n=1, a(1) = 20*1^2 = 20.
n=1, a(2) = 20*2^2 = 80.
n=1, a(3) = 20*3^2 = 180.
n=1, a(4) = 20*4^2 = 320.
...
(End)
MAPLE
a := n -> 20*n^2; seq(a(n), n=0..10^3); # Muniru A Asiru, Feb 01 2018
MATHEMATICA
20 Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 20, 80}, 50] (* Harvey P. Dale, Jan 18 2013 *)
PROG
(Magma) [20*n^2: n in [0..40]]; // Vincenzo Librandi, Sep 20 2011
(PARI) a(n) = 20*n^2 \\ Charles R Greathouse IV, Oct 07 2015
(GAP) List([0..10^3], n->20*n^2); # Muniru A Asiru, Feb 01 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 16 2011
STATUS
approved