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

%I A107245 #10 Feb 16 2025 08:32:57
%S A107245 0,0,0,0,0,0,1,2,6,22,86,342,1366,5462,21591,85600,339616,1347632,
%T A107245 5347632,21219888,84199984,334092848,1325649969,5260075594,
%U A107245 20871578510,82816815054,328610657230,1303901211854,5173777051854,20529140314318
%N A107245 Sum of squares of heptanacci numbers (Fibonacci 7-step numbers).
%C A107245 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.
%H A107245 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number.</a>
%H A107245 <a href="/index/Rec#order_29">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A107245 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.
%e A107245 a(0) = 0 = 0^2
%e A107245 a(1) = 0 = 0^2 + 0^2
%e A107245 a(2) = 0 = 0^2 + 0^2 + 0^2
%e A107245 a(3) = 0 = 0^2 + 0^2 + 0^2 + 0^2
%e A107245 a(4) = 0 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2
%e A107245 a(5) = 0 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2
%e A107245 a(6) = 1 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2
%e A107245 a(7) = 2 = 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 0^2 + 1^2 + 1^2
%e A107245 a(8) = 6 = 0^2 + 0^2 + 0^2+ 0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2
%e A107245 a(9) = 22 = 0^2 + 0^2 +0^2 + 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 = 2*11
%e A107245 a(10) = 86 = 8^2 + 22
%e A107245 a(11) = 342 = 16^2 + 86
%t A107245 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 *)
%t A107245 Accumulate[LinearRecurrence[{1,1,1,1,1,1,1},{0,0,0,0,0,0,1},30]^2] (* _Ray Chandler_, Aug 02 2015 *)
%Y A107245 Cf. A066178, A107239-A107244, A107246-A107248.
%K A107245 easy,nonn
%O A107245 0,8
%A A107245 _Jonathan Vos Post_, May 20 2005
%E A107245 a(14) inserted by _R. J. Mathar_, Aug 11 2009