%I A107239
%S A107239 0,0,1,2,6,22,71,240,816,2752,9313,31514,106590,360606,1219935,4126960,
%T A107239 13961456,47231280,159782161,540539330,1828631430,6186215574,
%U A107239 20927817799,70798300288,239508933824,810252920400,2741065994769
%N A107239 Sum of squares of tribonacci numbers (A000073).
%C A107239 Not to be confused with A107240 which is based on alternate tribonacci 
               sequence A000213(n), which starts 1,1,1,3. Prime values include: 
               a(4) = 2, a(7) = 71. Semiprime values include: a(5) = 6 = 2 * 3, 
               a(6) = 22 = 2 * 11, a(11) = 9313 = 67 * 139, a(35) = 3 * 15674342521439179.
%D A107239 M. Feinberg, "Fibonacci-Tribonacci." Fib. Quart. 1, 71-74, 1963.
%H A107239 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TribonacciNumber.html">Tribonacci Number.</a>.
%F A107239 a(n) = T(1)^2 + T(2)^2 + ... T(n)^2 where T(n) = A000073(n). a(0) = 0 
               and a(n+1) = a(n) + A000073(n+1).
%F A107239 a(n)=sum(i=0..n-2) A085697(i). G.f.: x^2*(1-x-x^2-x^3)/((x^3-x^2-x-1)(x^3+x^2+3*x-1)(1-x)). 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 19 2008]
%e A107239 a(1) = 0 = 0^2
%e A107239 a(2) = 0 = 0^2 + 0^2
%e A107239 a(3) = 1 = 0^2 + 0^2 + 1^2
%e A107239 a(4) = 2 = 0^2 + 0^2 + 1^2 + 1^2
%e A107239 a(5) = 6 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2
%e A107239 a(6) = 22 = 0^2 + 0^2 + 1^2 + 1^1 + 2^2 + 4^2
%e A107239 a(7) = 71 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 + 7^2
%e A107239 a(8) = 240 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 + 7^2 + 13^2
%e A107239 a(9) = 816 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 + 7^2 + 13^2 + 24^2
%e A107239 a(10) = 2752 = 44^2 + 816
%e A107239 a(11) = 9313 = 81^2 + 2752
%Y A107239 Cf. A000073, A000213, A107240, A107241-A107248.
%Y A107239 Sequence in context: A002839 A109194 A014334 this_sequence A148496 A106434 
               A150228
%Y A107239 Adjacent sequences: A107236 A107237 A107238 this_sequence A107240 A107241 
               A107242
%K A107239 easy,nonn
%O A107239 0,4
%A A107239 Jonathan Vos Post (jvospost3(AT)gmail.com), May 17 2005