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!)
A160999 Row sums of A027052. 2
1, 2, 5, 12, 31, 84, 233, 656, 1865, 5338, 15355, 44342, 128455, 373100, 1086087, 3167634, 9254009, 27074666, 79316491, 232633206, 683026535, 2007327660, 5904415195, 17381265934, 51203990457, 150945252394, 445252685313 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

a(n) = Sum_{k=0..2*n} A027052(n,k).

Conjecture: (-n+2)*a(n) +(6*n-11)*a(n-1) +(-7*n+1)*a(n-2) +2*(-4*n+27)*a(n-3) +(5*n-28)*a(n-4) +(2*n-3)*a(n-5) +3*(n-5)*a(n-6)=0. - R. J. Mathar, May 26 2016

EXAMPLE

a(2) = 1+0+1+2+1 = 5.

a(3) = 1+0+1+2+3+4+1 = 12.

MAPLE

A027052 := proc(n, k) option remember; if k =0 or k = 2*n then 1; elif k = 1 then 0; elif k =2 then 1; else procname(n-1, k-3)+procname(n-1, k-2)+procname(n-1, k-1) ; fi; end:

A160999 := proc(n) add( A027052(n, k), k=0..2*n) ; end: seq(A160999(n), n=0..30) ;

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==0 || k==2 || k==2*n, 1, If[k==1, 0, Sum[T[n-1, k-j], {j, 3}]]]; Table[Sum[T[n, k], {k, 0, 2*n}], {n, 0, 30}] (* G. C. Greubel, Nov 06 2019 *)

PROG

(Sage)

@CachedFunction

def T(n, k):

    if (k==0 or k==2 or k==2*n): return 1

    elif (k==1): return 0

    else: return sum(T(n-1, k-j) for j in (1..3))

[sum(T(n, k) for k in (0..2*n)) for n in (0..30)] # G. C. Greubel, Nov 06 2019

CROSSREFS

Sequence in context: A093379 A271929 A071359 * A014329 A045633 A090826

Adjacent sequences:  A160996 A160997 A160998 * A161000 A161001 A161002

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Jun 01 2009

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 May 25 07:29 EDT 2020. Contains 334584 sequences. (Running on oeis4.)