A143234 a(n) = sqrt(2^(-n)*A004003(n)) mod 32.

1, 1, 3, 29, 5, 5, 7, 25, 9, 9, 11, 21, 13, 13, 15, 17, 17, 17, 19, 13, 21, 21, 23, 9, 25, 25, 27, 5, 29, 29, 31, 1, 1, 1, 3, 29, 5, 5, 7, 25, 9, 9, 11, 21, 13, 13, 15, 17, 17, 17, 19, 13, 21, 21, 23, 9, 25, 25, 27, 5, 29, 29, 31, 1, 1, 1, 3, 29, 5, 5, 7, 25, 9, 9, 11, 21, 13, 13, 15, 17

Offset: 0

Author

Eric W. Weisstein, Jul 31 2008

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Domino Tiling
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A004003, A065072, A109613, A121262.

Programs

Magma

A143234:= func< n | (-1)^(0^((n+1) mod 4))*(2*Floor(n/2) + 1) mod 32 >;
[A143234(n): n in [0..100]]; // G. C. Greubel, Sep 11 2024

Mathematica

(* First program *)
a[n_]:= Mod[If[EvenQ[n], n + 1, (-1)^((n-1)/2)*n], 32];
Table[a[n], {n,0,100}]
(* Second program *)
A143234[n_]:= Mod[(-1)^(Floor[Mod[n,4]/3])*(2*Floor[n/2]+1), 32];
Table[A143234[n], {n,0,100}] (* G. C. Greubel, Sep 12 2024 *)

SageMath

def A143234(n): return ((-1)^(0^((n+1)%4))*(2*int(n//2)+1))%32
[A143234(n) for n in range(101)] # G. C. Greubel, Sep 11 2024

Formula

a(n) = A065072(n) mod 32.

From G. C. Greubel, Sep 12 2024: (Start)

a(n) = ( (-1)^A121262(n+1) * A109613(n) ) mod 32.

a(n) = a(n-32). (End)

Extensions

Offset changed by Editor(s) of Oeis.