A107246 Sum of squares of octanacci numbers (Fibonacci 8-step numbers).

0, 0, 0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 86871, 345952, 1378208, 5490992, 21877296, 87163696, 347276080, 1383600944, 5512434480, 21962292529, 87500852554, 348615720590, 1388934122190, 5533708922574, 22047074027470

Offset

0,9

Comments

Primes in this sequence include: a(8) = 2, a(17) = 280927. Semiprimes in this sequence include: a(9) = 6 = 2 * 3, a(10) = 22 = 2 * 11, a(11) = 86 = 2 * 43, a(13) = 1366 = 2 * 683, a(14) = 5462 = 2 * 2731, a(24) = 5512110374 = 2 * 2756055187, a(25) = 21961968423 = 3 * 7320656141, a(36) = 88177707994468342 = 2 * 44088853997234171.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Index entries for linear recurrences with constant coefficients, signature (3, 2, 4, 8, 14, 30, 60, 120, -266, -24, -38, -32, 120, -22, -50, -64, 136, 16, 30, 22, -68, 0, 10, 18, -28, 0, -6, -8, 14, 0, 0, -2, 2, 0, 0, 1, -1).

Formula

a(n) = F_8(0)^2 + F_8(1)^2 + ... F_8(n)^2, where F_8(n) = A079262(n).

Mathematica

Accumulate[LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 1}, 40]^2] (* Harvey P. Dale, May 25 2014 *)
LinearRecurrence[{3, 2, 4, 8, 14, 30, 60, 120, -266, -24, -38, -32, 120, -22, -50, -64, 136, 16, 30, 22, -68, 0, 10, 18, -28, 0, -6, -8, 14, 0, 0, -2, 2, 0, 0, 1, -1}, {0, 0, 0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 86871, 345952, 1378208, 5490992, 21877296, 87163696, 347276080, 1383600944, 5512434480, 21962292529, 87500852554, 348615720590, 1388934122190, 5533708922574, 22047074027470, 87838639467470, 349961474550734, 1394295671696334, 5555069815204303, 22132178477202944, 88177707994792448}, 31] (* Ray Chandler, Aug 02 2015 *)

Crossrefs

Cf. A079262, A107239-A107245, A107247-A107248.

Sequence in context: A107243 A107244 A107245 * A107247 A047849 A277222

Adjacent sequences: A107243 A107244 A107245 * A107247 A107248 A107249

Keyword

easy,nonn

Author

Jonathan Vos Post, May 27 2005

Extensions

Corrected from a(16) on by R. J. Mathar, Aug 11 2009

Status

approved