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A281813 a(0) = 3, a(n) = 8*n + 4 for n > 0.

%I A281813 #52 Jun 21 2025 13:31:43
%S A281813 3,12,20,28,36,44,52,60,68,76,84,92,100,108,116,124,132,140,148,156,
%T A281813 164,172,180,188,196,204,212,220,228,236,244,252,260,268,276,284,292,
%U A281813 300,308,316,324,332,340,348,356,364,372,380,388,396,404
%N A281813 a(0) = 3, a(n) = 8*n + 4 for n > 0.
%C A281813 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.
%H A281813 Rayan Ivaturi, <a href="/A281813/a281813_1.pdf">Ripple Numbers</a>
%H A281813 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A281813 G.f.: (3 + 6*x - x^2)/(1 - x)^2.
%F A281813 a(n) = A017113(n) for n>0, a(0) = 3.
%F A281813 a(n) = A086570(n+1) for n>=1. - _R. J. Mathar_, Jun 21 2025
%o A281813 /*
%o A281813 * This Java program generates the ripple number sequences (first 11 terms)
%o A281813 * for the seed values 1 to 9
%o A281813 */
%o A281813 /**
%o A281813 * @author Rayan Ivaturi
%o A281813 */
%o A281813 public class RippleNumbers {
%o A281813     public static void main(String[] args) {
%o A281813         int limit = 10;
%o A281813         for (int seed = 1; seed < limit; seed++) {
%o A281813             System.out.print("{" + seed);
%o A281813             int base = 2 * seed + 6;
%o A281813             System.out.print(", " + base);
%o A281813             for (int i = 1; i < limit; i++) {
%o A281813                 int ripple = base + 8 * i;
%o A281813                 System.out.print(", " + ripple);
%o A281813             }
%o A281813             System.out.println("}");
%o A281813         }
%o A281813     }
%o A281813 }
%o A281813 (PARI) a(n)=if(n>0, 8*n+4, 3) \\ _Charles R Greathouse IV_, Feb 07 2017
%Y A281813 Cf. A017113.
%Y A281813 Other 'ripple sequences': A022144 (s=1), A017089 (s=2).
%K A281813 nonn,easy,less
%O A281813 0,1
%A A281813 _Rayan Ivaturi_, Jan 30 2017
%E A281813 Entry revised by Editors of OEIS, Feb 09 2017