A133882 a(n) = binomial(n+2,n) mod 2^2.

1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1, 3, 2, 2, 3, 1, 0, 0, 1

Offset

0,2

Comments

Periodic with length 2^3 = 8.

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for linear recurrences with constant coefficients, signature (1, -1, 1, -1, 1, -1, 1).

Formula

a(n) = binomial(n+2,2) mod 2^2.

G.f.: (1 + 3*x + 2*x^2 + 2*x^3 + 3*x^4 + x^5)/(1-x^8).

G.f.: (1+x)*(1+2*x+2*x^3+x^4)/(1-x^8) = (1+2*x+2*x^3+x^4)/((1-x)*(1+x^2)*(1+x^4)).

a(n) = A105198(n+1). - R. J. Mathar, Jun 08 2008

Mathematica

Table[Mod[Binomial[n+2, n], 4], {n, 0, 120}]  (* Harvey P. Dale, Apr 16 2011 *)

Prog

(PARI) A133882(n) = (binomial(n+2, n) % 4); \\ Antti Karttunen, Aug 10 2017

Crossrefs

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133872, A133880, A133890, A133900, A133910.

For the sequence regarding "binomial(n+2, n) mod 2" see A133872.

A105198 shifted once left.

Sequence in context: A006379 A217956 A105198 * A092106 A278885 A183049

Adjacent sequences: A133879 A133880 A133881 * A133883 A133884 A133885

Keyword

nonn,easy

Author

Hieronymus Fischer, Oct 10 2007

Status

approved