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A107242 Sum of squares of tetranacci numbers (A001630).

%I A107242 #20 Feb 16 2025 08:32:57
%S A107242 0,0,1,5,14,50,194,723,2659,9884,36780,136636,507517,1885793,7006962,
%T A107242 26034006,96728470,359395319,1335332919,4961420008,18434129192,
%U A107242 68491926888,254481427113,945524491213,3513091674982,13052875206698
%N A107242 Sum of squares of tetranacci numbers (A001630).
%H A107242 W. C. Lynch, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/8-1/lynch.pdf">The t-Fibonacci numbers and polyphase sorting</a>, Fib. Quart., 8 (1970), pp. 6ff.
%H A107242 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TetranacciNumber.html">Tetranacci Number.</a>
%H A107242 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Fibonaccin-StepNumber.html">Fibonacci n-Step Number.</a>
%H A107242 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (3, 2, 2, 6, -16, -2, 6, -2, 2, 1, -1).
%F A107242 a(n) = F_4(1)^2 + F_4(1)^2 + F_4(2)^2 + ... F_4(n)^2 where F_4(n) = A001630(n). a(0) = 0, a(n+1) = a(n) + A001630(n)^2.
%F A107242 a(n)= 3*a(n-1) +2*a(n-2) +2*a(n-3) +6*a(n-4) -16*a(n-5) -2*a(n-6) +6*a(n-7) -2*a(n-8) +2*a(n-9) +a(n-10) -a(n-11). G.f.: x^2*(1+x)*(x^6-x^5-4*x^2+x+1)/((x-1) *(x^4+x^3-3*x^2-3*x+1) *(x^6-x^5+2*x^4-\ 2*x^3-2*x^2-x-1)). [_R. J. Mathar_, Aug 11 2009]
%e A107242 a(0) = 0 = 0^2,
%e A107242 a(1) = 0 = 0^2 + 0^2
%e A107242 a(2) = 1 = 0^2 + 0^2 + 1^2
%e A107242 a(3) = 5 = 0^2 + 0^2 + 1^2 + 2^2
%e A107242 a(4) = 14 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2
%e A107242 a(5) = 50 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2
%e A107242 a(6) = 194 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2 + 12^2
%e A107242 a(7) = 723 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2 + 12^2 + 23^2
%e A107242 a(8) = 2659 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2 + 12^2 + 23^2 + 44^2
%t A107242 Accumulate[LinearRecurrence[{1,1,1,1},{0,0,1,2},40]^2] (* or *) LinearRecurrence[{3,2,2,6,-16,-2,6,-2,2,1,-1},{0,0,1,5,14,50,194,723,2659,9884,36780},40] (* _Harvey P. Dale_, Aug 25 2013 *)
%Y A107242 Cf. A001630, A107239, A107243, A107244, A107245, A107246, A107247, A107248.
%K A107242 easy,nonn
%O A107242 0,4
%A A107242 _Jonathan Vos Post_, May 18 2005
%E A107242 a(13) and a(23) corrected by _R. J. Mathar_, Aug 11 2009