A167051 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

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

PROG

(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

CROSSREFS

Sequence in context: A182218 A093701 A045601 * A151661 A094599 A050082

Adjacent sequences: A167048 A167049 A167050 * A167052 A167053 A167054

KEYWORD

nonn

AUTHOR

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

STATUS

approved