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!)
A027947 a(n) = Sum_{k=m..n} T(k,n-k), where m = floor((n+1)/2); a(n) is the n-th diagonal-sum of left justified array T given by A027935. 1
1, 1, 2, 3, 4, 7, 9, 15, 21, 32, 48, 70, 107, 156, 236, 349, 521, 778, 1155, 1728, 2567, 3833, 5707, 8505, 12680, 18884, 28158, 41943, 62520, 93160, 138825, 206897, 308290, 459459, 684652, 1020311, 1520473, 2265815, 3376605 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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

FORMULA

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

MAPLE

seq(coeff(series((1+x)/(1-2*x^2-x^3+x^4), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 29 2019

MATHEMATICA

LinearRecurrence[{0, 2, 1, -1}, {1, 1, 2, 3}, 40] (* G. C. Greubel, Sep 29 2019 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((1+x)/(1-2*x^2-x^3+x^4)) \\ G. C. Greubel, Sep 29 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/(1-2*x^2-x^3+x^4) )); // G. C. Greubel, Sep 29 2019

(Sage)

def A027947_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P((1+x)/(1-2*x^2-x^3+x^4)).list()

A027947_list(40) # G. C. Greubel, Sep 29 2019

(GAP) a:=[1, 1, 2, 3];; for n in [5..40] do a[n]:=2*a[n-2]+a[n-3]-a[n-4]; od; a; # G. C. Greubel, Sep 29 2019

CROSSREFS

Cf. A027935.

Sequence in context: A108809 A276846 A303665 * A324736 A293853 A067236

Adjacent sequences:  A027944 A027945 A027946 * A027948 A027949 A027950

KEYWORD

nonn

AUTHOR

Clark Kimberling

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 3 10:49 EDT 2020. Contains 336198 sequences. (Running on oeis4.)