login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A054455 Row sums of triangle A054453. 3
1, 3, 7, 16, 34, 70, 140, 274, 527, 999, 1871, 3468, 6371, 11613, 21023, 37826, 67688, 120530, 213670, 377252, 663607, 1163361, 2033101, 3542808, 6157045, 10673703, 18460759, 31859716, 54872158, 94326622 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, 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

a(n) = Sum_{m=0..n} A054453(n, m).

a(n) = ((5*n^2 + 27*n + 50)*F(n+1) + 34*(n+1)*F(n))/50, F(n)= A000045(n) (Fibonacci numbers).

G.f.: ((Fib(x))^3)*(1-x^2)^2, with Fib(x)=1/(1-x-x^2) g.f. for A000045(n+1) (Fibonacci numbers without F(0)).

MATHEMATICA

LinearRecurrence[{3, 0, -5, 0, 3, 1}, {1, 3, 7, 16, 34, 70}, 40] (* or *) CoefficientList[Series[(1-x^2)^2/(1-x-x^2)^3, {x, 0, 40}], x] (* G. C. Greubel, Jan 31 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec((1-x^2)^2/(1-x-x^2)^3) \\ G. C. Greubel, Jan 31 2019

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (1-x^2)^2/(1-x-x^2)^3 )); // G. C. Greubel, Jan 31 2019

(Sage) ((1-x^2)^2/(1-x-x^2)^3).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 31 2019

(GAP) a:=[1, 3, 7, 16, 34, 70];; for n in [7..30] do a[n]:=3*a[n-1]-5*a[n-3] +3*a[n-5]+a[n-6]; od; a; # G. C. Greubel, Jan 31 2019

CROSSREFS

Cf. A054453, A000045.

Sequence in context: A014668 A182615 A181893 * A178455 A281811 A238089

Adjacent sequences:  A054452 A054453 A054454 * A054456 A054457 A054458

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang, Apr 27 2000

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 October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)