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A107242
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Sum of squares of tetranacci numbers (A001630).
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Not to be confused with A107241 [sum of squares of an alternate tetranacci sequence A000288(n) starting 1,1,1,1,4]. Prime values include: a(3) = 5, a(8) = 2659, a(33) = 474067074880054793. Semiprime values include: a(4) = 14 = 2 * 7, a(6) = 194 = 2 * 97, a(7) = 723 = 3 * 241, a(12) = 507517 = 317 * 1601, a(25) = 13052875206698 = 2 * 6526437603349, a(26) = 48497894765882 = 2 * 24248947382941.
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REFERENCES
| W. C. Lynch, The t-Fibonacci numbers and polyphase sorting, Fib. Quart., 8 (1970), pp. 6ff.
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LINKS
| Eric Weisstein's World of Mathematics, Tetranacci Number.
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number.
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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)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2009]
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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
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CROSSREFS
| Cf. A001630, A107239, A107243-A107248.
Sequence in context: A152051 A075827 A134418 * A203164 A063835 A054664
Adjacent sequences: A107239 A107240 A107241 * A107243 A107244 A107245
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 18 2005
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EXTENSIONS
| a(13) and a(23) corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2009
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