A167051 Start at 1, then add the first term (which is one here) plus 1 for the second term; then add the second term plus 2 for the third term; then add the third term to the sum of the first and second term; this gives the fourth term. Restart the sequence by adding 1 to the fourth term, etc. (From a sixth grade math extra credit assignment).

1, 2, 4, 7, 8, 10, 25, 26, 28, 79, 80, 82, 241, 242, 244, 727, 728, 730, 2185, 2186, 2188, 6559, 6560, 6562, 19681, 19682, 19684, 59047, 59048, 59050, 177145, 177146, 177148, 531439, 531440, 531442, 1594321, 1594322, 1594324, 4782967, 4782968, 4782970, 14348905

Offset: 1

Author

Chris Rice (cwrice(AT)research.att.com), Oct 27 2009

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Programs

PARI

seq(n)={my(a=vector(n)); a[1]=1; for(n=2, #a, my(t=n%3); a[n]=a[n-1]+if(t==2, 1, if(t==0, 2, a[n-2]+a[n-3]))); a} \\ Andrew Howroyd, Apr 13 2021

PARI

Vec((1 + 2*x + 4*x^2 + 3*x^3 - 6*x^5)/((1 - x)*(1 + x + x^2)*(1 - 3*x^3)) + O(x^40)) \\ Andrew Howroyd, Apr 13 2021

Formula

a(n) = a(n-1) + 1 for n mod 3 == 2;

a(n) = a(n-1) + 2 for n mod 3 == 0;

a(n) = a(n-1) + a(n-2) + a(n-3) for n mod 3 == 1 and n > 1.

G.f.: x*(1 + 2*x + 4*x^2 + 3*x^3 - 6*x^5)/((1 - x)*(1 + x + x^2)*(1 - 3*x^3)). - Andrew Howroyd, Apr 13 2021