0,3

A000073 is the tribonacci numbers. A113301 is the sum of odd-indexed terms of tribonacci numbers. A099463 is the bisection of the tribonacci numbers. A113300(n) + A113301(n) = cumulative sum of tribonacci numbers = A008937(n). Primes in A113300 include a(2) = 3, a(6) = 389, a(9) = 15061, a(10) = 50951. A113300 is semiprime for n = 3, 4, 5, 11, 14, ...

Partial sums of A099463. a(n+1) gives row sums of Riordan array (1/(1-x)^2,(1+x)^2/(1-x)^2)). Congruent to 0,1,1,0,0,1,1,0,0,... modulo 2. - Paul Barry (pbarry(AT)wit.ie), Feb 07 2006

a(n) = sum[from i = 0 to n] A000073(2*n). a(n) = sum[from i = 0 to n] A099463(n). A113300(n) + A113301(n) = A008937(n).

G.f.: 1/(1-3x-x^2-x^3); a(n)=3a(n-1)+a(n-2)+a(n-3). - Paul Barry (pbarry(AT)wit.ie), Feb 07 2006

a(0) = 0 = A000073(0)

a(1) = 0+1 = A000073(0) + A000073(2) = 1;

a(2) = 0+1+2 = A000073(0) + A000073(2) + A000073(4) = 3, prime;

a(3) = 0+1+2+7 = A000073(0) + A000073(2) + A000073(4) + A000073(6) = 10 = 2*5, semiprime;

a(4) = 0+1+2+7+24 = A000073(0) + A000073(2) + A000073(4) + A000073(6) + A000073(8) = 34 = 2 * 17, semiprime;

a(5) = 1+2+7+24+81 = 115 = 5 * 23, semiprime.

Cf. A000073, A008937, A099463, A113301.

Adjacent sequences: A113297 A113298 A113299 this_sequence A113301 A113302 A113303

Sequence in context: A041633 A034215 A083580 this_sequence A007052 A048580 A059738

easy,nonn

Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 24 2005

More terms from Paul Barry (pbarry(AT)wit.ie), Feb 07 2006