A107245 Sum of squares of heptanacci numbers (Fibonacci 7-step numbers).

0, 0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5462, 21591, 85600, 339616, 1347632, 5347632, 21219888, 84199984, 334092848, 1325649969, 5260075594, 20871578510, 82816815054, 328610657230, 1303901211854, 5173777051854, 20529140314318

Offset: 0

Author

Jonathan Vos Post, May 20 2005

Keywords

• easy
• nonn

Comments

Primes include: a(7) = 2. Semiprimes include a(8) = 6 = 2 * 3, a(9) = 22 = 2 * 11, a(10) = 86 = 2 * 43, a(12) = 1366 = 2 * 683, a(13) = 5462 = 2 * 2731.

Examples

			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) = 0 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2
a(6) = 1 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2
a(7) = 2 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2
a(8) = 6 = 0^2 + 0^2 + 0^2+ 0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2
a(9) = 22 = 0^2 + 0^2 +0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 = 2*11
a(10) = 86 = 8^2 + 22
a(11) = 342 = 16^2 + 86
		

Links

• Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
• Index entries for linear recurrences with constant coefficients, signature (3, 2, 4, 7, 15, 30, 60, -131, -9, -8, 28, -11, -25, -32, 68, 5, 5, -10, 0, 5, 9, -14, 0, -1, 1, 0, 0, -1, 1).

Crossrefs

Cf. A066178, A107239-A107244, A107246-A107248.

Programs

Mathematica

LinearRecurrence[{3, 2, 4, 7, 15, 30, 60, -131, -9, -8, 28, -11, -25, -32, 68, 5, 5, -10, 0, 5, 9, -14, 0, -1, 1, 0, 0, -1, 1},{0, 0, 0, 0, 0, 0, 1, 2, 6, 22, 86, 342, 1366, 5462, 21591, 85600, 339616, 1347632, 5347632, 21219888, 84199984, 334092848, 1325649969, 5260075594, 20871578510, 82816815054, 328610657230, 1303901211854, 5173777051854},30] (* Ray Chandler, Aug 02 2015 *)
Accumulate[LinearRecurrence[{1,1,1,1,1,1,1},{0,0,0,0,0,0,1},30]^2] (* Ray Chandler, Aug 02 2015 *)

Formula

a(n) = F_7(0)^2 + F_7(1)^2 + ... F_7(n)^2, note that F_7(n) = A066178(n) with corrected offset (from leading zeros). a(0) = 0, a(n+1) = a(n) + F_7(n)^2.

Extensions

a(14) inserted by R. J. Mathar, Aug 11 2009