A160999 Row sums of A027052.

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

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