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

Author

Jonathan Vos Post, May 27 2005

Keywords

• easy
• nonn

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).

Crossrefs

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

Programs

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 *)

Formula

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

Extensions

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