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A281813 a(0) = 3, a(n) = 8*n + 4 for n > 0. 1
3, 12, 20, 28, 36, 44, 52, 60, 68, 76, 84, 92, 100, 108, 116, 124, 132, 140, 148, 156, 164, 172, 180, 188, 196, 204, 212, 220, 228, 236, 244, 252, 260, 268, 276, 284, 292, 300, 308, 316, 324, 332, 340, 348, 356, 364, 372, 380, 388, 396, 404 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..50.

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

Cf. A017113.

Other 'ripple sequences': A022144 (s=1), A017089 (s=2).

Sequence in context: A199129 A257942 A063244 * A063102 A122576 A212760

Adjacent sequences:  A281810 A281811 A281812 * A281814 A281815 A281816

KEYWORD

nonn,easy,less

AUTHOR

Rayan Ivaturi, Jan 30 2017

EXTENSIONS

Entry revised by Editors of OEIS, Feb 09 2017

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)