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A107240 Sum of squares of first n tribonacci numbers (A000213). 4
1, 2, 3, 12, 37, 118, 407, 1368, 4617, 15642, 52891, 178916, 605325, 2047726, 6927407, 23435376, 79281105, 268206130, 907335091, 3069492092, 10384017717, 35128880742, 118840150983, 402033352264, 1360069089113, 4601080768074 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is prime for n = 2, 3, 5, 15, 29, ...

a(n) is semiprime for n = 7, 11, 21, 33, ...

For Fibonacci numbers (A000045) F(i) we have Sum_{i=1..n} F(i) = F(n)*F(n+1).

LINKS

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

M. Feinberg, Fibonacci-Tribonacci, Fib. Quart. 1(3) (1963), 71-74.

Eric Weisstein's World of Mathematics, Tribonacci Number.

Index entries for linear recurrences with constant coefficients, signature (3, 1, 3, -7, 1, -1, 1).

FORMULA

a(n) = Sum_{i=1..n} A000213(i)^2.

a(n)= 3*a(n-1) +a(n-2) +3*a(n-3) -7*a(n-4) +a(n-5) -a(n-6) +a(n-7). G.f.: (x^3-x^2+3*x-1)*(1+x)^2/((x-1)*(x^3+x^2+3*x-1)*(x^3-x^2-x-1)). [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 + 3^2 = 12.

a(5) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 = 37, prime.

a(6) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 + 9^2 = 118 = 2 * 59, semiprime.

a(7) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 + 9^2 + 17^2 = 407 = 11 * 37, semiprime.

MATHEMATICA

Accumulate[LinearRecurrence[{1, 1, 1}, {1, 1, 1}, 30]^2] (* Harvey P. Dale, Nov 11 2011 *)

LinearRecurrence[{3, 1, 3, -7, 1, -1, 1}, {1, 2, 3, 12, 37, 118, 407}, 26] (* Ray Chandler, Aug 02 2015 *)

CROSSREFS

Cf. A000213, A107240, A107239-A107248.

Sequence in context: A165301 A072440 A135522 * A099171 A268561 A012307

Adjacent sequences:  A107237 A107238 A107239 * A107241 A107242 A107243

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 14 2005

STATUS

approved

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Last modified May 14 16:48 EDT 2021. Contains 343898 sequences. (Running on oeis4.)