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

0,9

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

Table of n, a(n) for n=0..30.

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).

Formula

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

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 *)

Crossrefs

Cf. A104144, A107239-A107246, A107248.

Sequence in context: A107244 A107245 A107246 * A047849 A277222 A150256

Adjacent sequences: A107244 A107245 A107246 * A107248 A107249 A107250

Keyword

easy,nonn

Author

Jonathan Vos Post, May 29 2005

Status

approved