A107242 Sum of squares of tetranacci numbers (A001630).

0, 0, 1, 5, 14, 50, 194, 723, 2659, 9884, 36780, 136636, 507517, 1885793, 7006962, 26034006, 96728470, 359395319, 1335332919, 4961420008, 18434129192, 68491926888, 254481427113, 945524491213, 3513091674982, 13052875206698

Offset

0,4

Links

Table of n, a(n) for n=0..25.

W. C. Lynch, The t-Fibonacci numbers and polyphase sorting, Fib. Quart., 8 (1970), pp. 6ff.

Eric Weisstein's World of Mathematics, Tetranacci Number.

Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.

Index entries for linear recurrences with constant coefficients, signature (3, 2, 2, 6, -16, -2, 6, -2, 2, 1, -1).

Formula

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.

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]

Example

a(0) = 0 = 0^2,
a(1) = 0 = 0^2 + 0^2
a(2) = 1 = 0^2 + 0^2 + 1^2
a(3) = 5 = 0^2 + 0^2 + 1^2 + 2^2
a(4) = 14 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2
a(5) = 50 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2
a(6) = 194 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2 + 12^2
a(7) = 723 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2 + 12^2 + 23^2
a(8) = 2659 = 0^2 + 0^2 + 1^2 + 2^2 + 3^2 + 6^2 + 12^2 + 23^2 + 44^2

Mathematica

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 *)

Crossrefs

Cf. A001630, A107239, A107243, A107244, A107245, A107246, A107247, A107248.

Sequence in context: A134418 A272147 A272223 * A203164 A063835 A054664

Adjacent sequences: A107239 A107240 A107241 * A107243 A107244 A107245

Keyword

easy,nonn

Author

Jonathan Vos Post, May 18 2005

Extensions

a(13) and a(23) corrected by R. J. Mathar, Aug 11 2009

Status

approved