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 A107244 Sum of squares of hexanacci numbers (A001592, Fibonacci 6-step numbers). 2
 0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5335, 20960, 82464, 324528, 1277104, 5025200, 19770800, 77789489, 306071370, 1204272270, 4738336974, 18643463374, 73354544590, 288620849614, 1135607911375, 4468164041216, 17580442344960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Primes include: a(6) = 2. Semiprimes include a(7) = 6 = 2 * 3, a(8) = 22 = 2 * 11, a(9) = 86 = 2 * 43, a(11) = 1366 = 2 * 683, a(19) = 77789489 = 3989 * 19501, a(23) = 18643463374 = 2 * 9321731687, LINKS Eric Weisstein's World of Mathematics, Fibonacci n-Step Number. FORMULA a(n) = F_6(0)^2 + F_6(1)^2 + ... F_6(n)^2, where F_6(n) = A001592(n). a(0) = 0, a(n+1) = a(n) + A001592(n). a(n)= 3*a(n-1) +2*a(n-2) +4*a(n-3) +6*a(n-4) +14*a(n-5) +28*a(n-6) -67*a(n-7) -9*a(n-8) -8*a(n-9) +28*a(n-10) -8*a(n-11) -12*a(n-12) +20*a(n-13) +5*a(n-14) +5*a(n-15) -10*a(n-16) +2*a(n-18) -2*a(n-19) -a(n-21) +a(n-22). [From R. J. Mathar, Aug 11 2009] EXAMPLE a(0) = 0 = 0^2 a(1) = 0 = 0^2 + 0^2 a(2) = 0 = 0^2 + 0^2 + 0^2 a(3) = 0 = 0^2 + 0^2 + 0^2 + 0^2 a(4) = 0 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 a(5) = 1 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2 a(6) = 2 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2 a(7) = 6 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2 a(8) = 22 = 0^2 + 0^2 +0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 MATHEMATICA Accumulate[LinearRecurrence[{1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 1}, 50]^2] (* From Harvey P. Dale, Jan 19 2012 *) CROSSREFS Cf. A001592, A107239-A107243, A107245-A107248. Sequence in context: A029759 A150255 A107243 * A107245 A107246 A107247 Adjacent sequences:  A107241 A107242 A107243 * A107245 A107246 A107247 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, May 19 2005 STATUS approved

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