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A107241 Sum of squares of first n tetranacci numbers (A000288). 2
1, 2, 3, 4, 20, 69, 238, 863, 3264, 12100, 44861, 166662, 619591, 2301800, 8551800, 31774561, 118060082, 438649107, 1629796276, 6055504952, 22499207241, 83595676570, 310599326171, 1154030334396, 4287794153932, 15931278338957 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Tetranacci numbers are also called Fibonacci 4-step numbers. a(n) is prime for n = 2, 3, 8, 26, ... a(n) is semiprime for n = 4, 6, 11, 13, ... a(10) = 12100 = 94^2 + 3264 = 110^2 = 2^2 * 5^2 * 11^2. For Fibonacci numbers (A000045) F(i) we have SUM[from i=1 to n]F(i) = F(n)*F(n+1).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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) = SUM[from i=1 to n][A000288(i)]^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.: (1-x-5*x^2-11*x^3-8*x^4-x^5-x^6-7*x^7+x^8+4*x^9)/((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, Aug 11 2009]

EXAMPLE

a(1) = 1^2 = 1.

a(2) = 1^2 + 1^2 = 1.

a(3) = 1^2 + 1^2 + 1^2 = 3, prime.

a(4) = 1^2 + 1^2 + 1^2 + 1^2 = 4 = 2^2, semiprime.

a(5) = 1^2 + 1^2 + 1^2 + 1^2 + 4^2 = 20.

a(6) = 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 7^2 = 69 = 3 * 23, semiprime.

a(8) = 1^2 + 1^2 + 1^2 + 1^2 + 4^2 + 7^2 + 13^2 + 25^2 = 863, prime.

MATHEMATICA

Accumulate[LinearRecurrence[{1, 1, 1, 1}, {1, 1, 1, 1}, 30]^2] (* Harvey P. Dale, Feb 14 2012 *)

LinearRecurrence[{3, 2, 2, 6, -16, -2, 6, -2, 2, 1, -1}, {1, 2, 3, 4, 20, 69, 238, 863, 3264, 12100, 44861}, 26] (* Ray Chandler, Aug 02 2015 *)

CROSSREFS

Cf. A000288, A107239-A107248.

Sequence in context: A012578 A012573 A268349 * A012576 A012579 A012283

Adjacent sequences:  A107238 A107239 A107240 * A107242 A107243 A107244

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 14 2005

STATUS

approved

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Last modified February 20 04:27 EST 2018. Contains 299358 sequences. (Running on oeis4.)