login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086926 Product of Fibonacci and (shifted) triangular numbers. 2
0, 0, 1, 6, 18, 50, 120, 273, 588, 1224, 2475, 4895, 9504, 18174, 34307, 64050, 118440, 217192, 395352, 714951, 1285350, 2298660, 4091241, 7250221, 12797568, 22507500, 39452725, 68942718, 120132558, 208776974, 361937400, 626015085, 1080441264 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,0,-5,0,3,1).

FORMULA

From Franklin T. Adams-Watters, Feb 03 2006: (Start)

a(n) = A000045(n)*A000217(n-1) = A000045(n)*n*(n-1)/2.

a(n) = (n/(n-2)*a(n-1) + n*(n-1))/((n-2)*(n-3))*a(n-2).

G.f.: x^2*(1+3x+x^3)/(1-x-x^2)^3. (End)

a(n) = Sum_{k=0..n-1} Sum_{i=0..n-1} i * C(n-k-1,k). - Wesley Ivan Hurt, Sep 19 2017

From Colin Barker, Sep 20 2017: (Start)

a(n) = ((-1)*(2^(-1-n)*((1-sqrt(5))^n - (1+sqrt(5))^n)*(-1+n)*n)) / sqrt(5).

a(n) = 3*a(n-1) - 5*a(n-3) + 3*a(n-5) + a(n-6) for n>5. (End)

MATHEMATICA

Array[Fibonacci[#] PolygonalNumber[# - 1] &, 33, 0] (* or *)

LinearRecurrence[{3, 0, -5, 0, 3, 1}, {0, 0, 1, 6, 18, 50}, 33] (* or *)

CoefficientList[Series[x^2*(1 + 3 x + x^3)/(1 - x - x^2)^3, {x, 0, 32}], x] (* Michael De Vlieger, Dec 17 2017 *)

PROG

(MuPAD) numlib::fibonacci(n)*binomial(n, 2) $ n = 0..35; // Zerinvary Lajos, May 09 2008

(PARI) concat(vector(2), Vec(x^2*(1 + 3*x + x^3) / (1 - x - x^2)^3 + O(x^40))) \\ Colin Barker, Sep 20 2017

CROSSREFS

Cf. A000045, A000217, A045925.

Sequence in context: A099857 A163765 A179754 * A328534 A003290 A318160

Adjacent sequences:  A086923 A086924 A086925 * A086927 A086928 A086929

KEYWORD

nonn,easy

AUTHOR

James FitzSimons (cherry(AT)getnet.net), Sep 20 2003

EXTENSIONS

Definition and more terms from Franklin T. Adams-Watters, Feb 03 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 4 03:57 EDT 2021. Contains 346442 sequences. (Running on oeis4.)