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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053311 Partial sums of A000285. 4
1, 5, 10, 19, 33, 56, 93, 153, 250, 407, 661, 1072, 1737, 2813, 4554, 7371, 11929, 19304, 31237, 50545, 81786, 132335, 214125, 346464, 560593, 907061, 1467658, 2374723, 3842385, 6217112, 10059501, 16276617, 26336122 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., pp. 189, 194-196.

J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 224.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

FORMULA

a(n) = a(n-1) + a(n-2) + 4; a(0)=1, a(1)=5; n >= 1.

a(n) = 4*F(n+2) + F(n+1) - 4, where F(k) is A000045(k).

From R. J. Mathar, Apr 29 2013: (Start)

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

a(n) = A000071(n+3) + 3*A000071(n+2) = A000285(n+2) - 4. (End)

MATHEMATICA

CoefficientList[Series[(1+3*x)/((x-1)*(x^2+x-1)), {x, 0, 50}], x] (* G. C. Greubel, May 24 2018 *)

PROG

(PARI) x='x+O('x^30); Vec((1+3*x)/((x-1)*(x^2+x-1))) \\ G. C. Greubel, May 24 2018

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x)/((x-1)*(x^2+x-1)))); // G. C. Greubel, May 24 2018

CROSSREFS

Cf. A000285.

a(n) = A101220(4, 1, n+1).

Sequence in context: A191595 A047882 A184260 * A147390 A300019 A115825

Adjacent sequences:  A053308 A053309 A053310 * A053312 A053313 A053314

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Mar 06 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 18 14:29 EDT 2018. Contains 316321 sequences. (Running on oeis4.)