login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A133883 a(n) = binomial(n+3,n) mod 3^2. 6
1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 0, 0, 0, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 0, 0, 0, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8, 0, 0, 0, 1, 4, 1, 2, 8, 2, 3, 3, 3, 4, 7, 4, 5, 2, 5, 6, 6, 6, 7, 1, 7, 8, 5, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Periodic with length 3^3 = 27.

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = binomial(n+3,3) mod 3^2.

G.f.: (1 +3*x -3*x^2 +2*x^3 +9*x^4 -9*x^5 +3*x^6 +9*x^7 -9*x^8 +4*x^9 +12*x^10 -12*x^11 +5*x^12 +9*x^13 -9*x^14 +6*x^15 +9*x^16 -9*x^17 +7*x^18 +3*x^19 -3*x^20 +8*x^21) / ((1 -x)*(1 +x^3 +x^6)*(1 +x^9 +x^18)). - Colin Barker, Jul 19 2016

MATHEMATICA

Table[Mod[Binomial[n + 3, n], 9], {n, 0, 120}] (* or *)

CoefficientList[Series[(1 + 3 x - 3 x^2 + 2 x^3 + 9 x^4 - 9 x^5 + 3 x^6 + 9 x^7 - 9 x^8 + 4 x^9 + 12 x^10 - 12 x^11 + 5 x^12 + 9 x^13 - 9 x^14 + 6 x^15 + 9 x^16 - 9 x^17 + 7 x^18 + 3 x^19 - 3 x^20 + 8 x^21)/((1 - x) (1 + x^3 + x^6) (1 + x^9 + x^18)), {x, 0, 120}], x] (* Michael De Vlieger, Jul 19 2016 *)

PROG

(PARI) Vec((1 +3*x -3*x^2 +2*x^3 +9*x^4 -9*x^5 +3*x^6 +9*x^7 -9*x^8 +4*x^9 +12*x^10 -12*x^11 +5*x^12 +9*x^13 -9*x^14 +6*x^15 +9*x^16 -9*x^17 +7*x^18 +3*x^19 -3*x^20 +8*x^21) / ((1 -x)*(1 +x^3 +x^6)*(1 +x^9 +x^18)) + O(x^200)) \\ Colin Barker, Jul 19 2016

(MAGMA) [Binomial(n+3, n) mod 9: n in [0..60]]; // Vincenzo Librandi, Jul 20 2016

CROSSREFS

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

Cf. A133873, A133880, A133890, A133900, A133910.

For the sequence regarding "Binomial(n+3, n) mod 3" see A133873.

Sequence in context: A120578 A096249 A081454 * A279816 A004160 A128077

Adjacent sequences:  A133880 A133881 A133882 * A133884 A133885 A133886

KEYWORD

nonn,easy

AUTHOR

Hieronymus Fischer, Oct 10 2007

EXTENSIONS

Corrected g.f. by Colin Barker, Jul 19 2016

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 23 14:17 EDT 2019. Contains 321431 sequences. (Running on oeis4.)