OFFSET
0,1
COMMENTS
Consider a 1 X S rectangle on an infinite grid and surround it successively with the minimum number of 1 X 1 tiles: the initial S on step 0, 2S + 6 on step 1, 2S + 14 on step 2, and so on. This sequence is case S = 3. See Ivaturi link for a connection to sieving for primes.
LINKS
Rayan Ivaturi, Ripple Numbers
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
G.f.: (3 + 6*x - x^2)/(1 - x)^2.
a(n) = A017113(n) for n>0, a(0) = 3.
PROG
/*
* This Java program generates the ripple number sequences (first 11 terms)
* for the seed values 1 to 9
*/
/**
* @author Rayan Ivaturi
*/
public class RippleNumbers {
public static void main(String[] args) {
int limit = 10;
for (int seed = 1; seed < limit; seed++) {
System.out.print("{" + seed);
int base = 2 * seed + 6;
System.out.print(", " + base);
for (int i = 1; i < limit; i++) {
int ripple = base + 8 * i;
System.out.print(", " + ripple);
}
System.out.println("}");
}
}
}
(PARI) a(n)=if(n>0, 8*n+4, 3) \\ Charles R Greathouse IV, Feb 07 2017
CROSSREFS
KEYWORD
nonn,easy,less
AUTHOR
Rayan Ivaturi, Jan 30 2017
EXTENSIONS
Entry revised by Editors of OEIS, Feb 09 2017
STATUS
approved