|
| |
|
|
A113300
|
|
Sum of even-indexed terms of tribonacci numbers.
|
|
6
| |
|
|
0, 1, 3, 10, 34, 115, 389, 1316, 4452, 15061, 50951, 172366, 583110, 1972647, 6673417, 22576008, 76374088, 258371689, 874065163, 2956941266, 10003260650, 33840788379, 114482567053, 387291750188, 1310198605996, 4432370135229, 14994600761871, 50726371026838
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| 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
|
|
|
FORMULA
| 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
|
|
|
EXAMPLE
| 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.
|
|
|
MATHEMATICA
| Accumulate[Take[LinearRecurrence[{1, 1, 1}, {0, 0, 1}, 60], {1, -1, 2}]] (* From Harvey P. Dale, Nov 06 2011 *)
LinearRecurrence[{3, 1, 1}, {0, 1, 3}, 40] (* From Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)
|
|
|
CROSSREFS
| Cf. A000073, A008937, A099463, A113301.
Sequence in context: A034215 A193036 A083580 * A007052 A048580 A059738
Adjacent sequences: A113297 A113298 A113299 * A113301 A113302 A113303
|
|
|
KEYWORD
| easy,nonn,changed
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 24 2005
|
|
|
EXTENSIONS
| More terms from Paul Barry (pbarry(AT)wit.ie), Feb 07 2006
|
| |
|
|
