A107244 Sum of squares of hexanacci numbers (A001592, Fibonacci 6-step numbers).

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

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

Table of n, a(n) for n=0..28.

Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.

Index entries for linear recurrences with constant coefficients, signature (3, 2, 4, 6, 14, 28, -67, -9, -8, 28, -8, -12, 20, 5, 5, -10, 0, 2, -2, 0, -1, 1).

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] (* Harvey P. Dale, Jan 19 2012 *)
LinearRecurrence[{3, 2, 4, 6, 14, 28, -67, -9, -8, 28, -8, -12, 20, 5, 5, -10, 0, 2, -2, 0, -1, 1}, {0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5335, 20960, 82464, 324528, 1277104, 5025200, 19770800, 77789489, 306071370, 1204272270}, 29] (* Ray Chandler, Aug 02 2015 *)

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