A107247 Sum of squares of nonacci numbers (Fibonacci 9-step numbers).

0, 0, 0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5462, 21846, 87382, 348503, 1390944, 5552544, 22166320, 88491056, 353269040, 1410299184, 5630100784, 22476064048, 89727075632, 358201316657, 1429983219018, 5708667195022, 22789694921422

Offset: 0

Author

Jonathan Vos Post, May 29 2005

Keywords

• easy
• nonn

Comments

Primes in this sequence include: a(9) = 2, which is next? Semiprimes in this sequence include: a(10) = 6 = 2 * 3, a(11) = 22 = 2 * 11, a(12) = 86 = 2 * 43, a(14) = 1366 = 2 * 683, a(15) = 5462 = 2 * 2731, a(17) = 87382 = 2 * 43691, a(18) = 348503 = 37 * 9419, a(28) = 358201316657 = 71 * 5045088967.

Links

• Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
• Index entries for linear recurrences with constant coefficients, signature (3, 2, 4, 8, 15, 31, 62, 124, 248, -522, -24, -38, -32, 120, -26, -68, -138, -160, 392, 16, 30, 22, -68, 0, 16, 50, 58, -124, 0, -6, -8, 14, 0, 0, -6, -12, 18, 0, 0, 1, -1, 0, 0, 0, 1, -1).

Crossrefs

Cf. A104144, A107239-A107246, A107248.

Programs

Mathematica

Accumulate[LinearRecurrence[{1,1,1,1,1,1,1,1,1},{0,0,0,0,0,0,0,0,1},31]^2]  (* Ray Chandler, Aug 02 2015 *)

Formula

a(n) = F_9(0)^2 + F_9(1)^2 + ... F_9(n)^2, where F_9(n) = A104144(n).