A133884 - OEIS

A133884

a(n) = binomial(n+4,n) mod 4.

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

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OFFSET

0,3

COMMENTS

Periodic with length 4^2=16.

LINKS

Table of n, a(n) for n=0..104.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -1, 1).

FORMULA

a(n) = binomial(n+4,4) mod 4.

G.f.: (1 + x + 3*x^2 + 3*x^3 + 2*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + 3*x^8 + 3*x^9 + x^10 + x^11)/(1 - x^16) = (1 + 2*x^2 + 2*x^6 + x^8)/((1 - x)*(1 + x^4)*(1 + x^8)).

a(n) = A000505(n+5) mod 4. - John M. Campbell, Jul 14 2016

a(n) = A000506(n+6) mod 4. - John M. Campbell, Jul 15 2016

EXAMPLE

For n=2, binomial(6,2) = 6*5/2 = 15, which is 3 (mod 4) so a(2) = 3. - Michael B. Porter, Jul 19 2016

MATHEMATICA

Table[Mod[Binomial[n + 4, 4], 4], {n, 0, 100}] (* Vincenzo Librandi, Jul 15 2016 *)

PROG

(Magma) [Binomial(n+4, n) mod 4: n in [0..100]]; // Vincenzo Librandi, Jul 15 2016

CROSSREFS

Cf. A000040, A133630, A038509.

Cf. A133620, A133621, A133622, A133623, A133624, A133625

Cf. A133634, A133635, A133636.