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A200541 Product of Fibonacci and tribonacci numbers: a(n) = A000045(n+1)*A000073(n+2). 1
1, 1, 4, 12, 35, 104, 312, 924, 2754, 8195, 24386, 72576, 215991, 642785, 1912960, 5693016, 16942573, 50421592, 150056090, 446571180, 1329008590, 3955167387, 11770690808, 35029911168, 104250013425, 310251009501, 923315841860, 2747814245904, 8177573467339, 24336691577000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit a(n+1)/a(n) = (sqrt(5)+1)/2 * (1+(19+3*sqrt(33))^(1/3)+(19-3*sqrt(33))^(1/3))/3 = 2.9760284849940...

LINKS

Paul D. Hanna, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (1,4,5,2,-1,1).

FORMULA

G.f.: (1 - x^2 - x^3) / (1 - x - 4*x^2 - 5*x^3 - 2*x^4 + x^5 - x^6).

EXAMPLE

G.f.: A(x) = 1 + x + 4*x^2 + 12*x^3 + 35*x^4 + 104*x^5 + 312*x^6 + 924*x^7 + 2754*x^8 +...+ A000045(n+1)*A000073(n+2)*x^n +...

where tribonacci numbers (A000073) begin:

[1,1,2,4,7,13,24,44,81,149,274,504,927,1705,3136,5768,10609,...],

and Fibonacci numbers (A000045) begin:

[1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,1597,2584,...].

MATHEMATICA

Module[{nn=30, fs, ts}, fs=Fibonacci[Range[nn]]; ts=LinearRecurrence[{1, 1, 1}, {1, 1, 2}, nn]; Times@@@Thread[{fs, ts}]] (* or *) LinearRecurrence[ {1, 4, 5, 2, -1, 1}, {1, 1, 4, 12, 35, 104}, 30] (* Harvey P. Dale, Dec 14 2016 *)

PROG

(PARI) {a(n)=polcoeff((1-x^2-x^3)/(1-x-4*x^2-5*x^3-2*x^4+x^5-x^6 +x*O(x^n)), n)}

(PARI) {A000073(n)=polcoeff(x^2/(1-x-x^2-x^3+x^3*O(x^n)), n)}

{a(n)=fibonacci(n+1)*A000073(n+2)}

CROSSREFS

Cf. A001582, A000045, A000073.

Sequence in context: A035045 A196859 A090328 * A149318 A233181 A053595

Adjacent sequences:  A200538 A200539 A200540 * A200542 A200543 A200544

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 18 2011

STATUS

approved

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Last modified October 21 05:28 EDT 2021. Contains 348141 sequences. (Running on oeis4.)