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A107245
Sum of squares of heptanacci numbers (Fibonacci 7-step numbers).
6
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
0,8
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.
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).
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.
EXAMPLE
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
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, May 20 2005
EXTENSIONS
a(14) inserted by R. J. Mathar, Aug 11 2009
STATUS
approved