A024692 - OEIS

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A024692

a(n) = s(1)s(n) + s(2)s(n-1) +... + s(k)s(n+1-k), where k = floor((n+1)/2), s =A023533.

10

1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,139

LINKS

G. C. Greubel,Table of n, a(n) for n = 1..5000

FORMULA

a(n) = Sum_{k=1..floor((n+1)/2)}A023533(k)*A023533(n-k+1).

MATHEMATICA

A023533[n_]:=A023533[n]= If[Binomial[Floor[Surd[6*n-1, 3]] +2, 3]!= n, 0, 1];

A024692[n_]:=A024692[n]= Sum[A023533[k]*A023533[n+1-k], {k, Floor[(n+1)/2]}];

Table[A024692[n], {n, 100}] (*G. C. Greubel,Jul 14 2022 *)

PROG

(Magma)

A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;

[(&+[A023533(k)*A023533(n-k+1): k in [1..Floor((n+1)/2)]]): n in [1..100]]; //G. C. Greubel,Jul 14 2022

(SageMath)

defA023533(n):

if binomial( floor( (6*n-1)^(1/3) ) +2, 3)!= n: return 0

else: return 1

[sum(A023533(k)*A023533(n-k+1) for k in (1..((n+1)//2))) for n in (1..100)] #G. C. Greubel,Jul 14 2022

CROSSREFS

Sequence in context:A037011 A070563 A374053*A373604 A079978 A164704

Adjacent sequences:A024689 A024690 A024691*A024693 A024694 A024695

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved