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A025075 a(n) = s(1)*t(n+1) + s(2)*t(n) + ... + s(k)*t(n-k+2), where k = floor((n+1)/2), s = A023532, t = A023533. 2
0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,34

LINKS

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

FORMULA

a(n)_= Sum_{k=1..floor((n+1)/2)} A023532(k) * A023533(n-k+2).

MATHEMATICA

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

A023532[n_]:= If[IntegerQ[(Sqrt[8*n+9] -3)/2], 0, 1];

A025075[n_]:= A025075[n]= Sum[A023532[j]*A023533[n-j+2], {j, Floor[(n+1)/2]}];

Table[A025075[n], {n, 130}] (* G. C. Greubel, Aug 02 2022 *)

PROG

(Magma)

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

A023532:= func< n |  IsSquare(8*n+9) select 0 else 1 >;

A025075:= func< n | (&+[A023532(k)*A023533(n+2-k): k in [1..Floor((n+1)/2)]]) >;

[A025075(n): n in [1..130]]; // G. C. Greubel, Aug 02 2022

(SageMath)

@CachedFunction

def A023533(n): return 0 if (binomial( floor( (6*n-1)^(1/3) ) +2, 3) != n) else 1

def A023532(n): return 0 if is_square(8*n+9) else 1

def A025075(n): return sum(A023532(k)*A023533(n-k+2) for k in (1..((n+1)//2)))

[A025075(n) for n in (1..130)] # G. C. Greubel, Aug 02 2022

CROSSREFS

Cf. A023532, A023533.

Sequence in context: A276321 A152196 A024375 * A175609 A038717 A073267

Adjacent sequences:  A025072 A025073 A025074 * A025076 A025077 A025078

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified September 29 00:44 EDT 2022. Contains 357081 sequences. (Running on oeis4.)