A213029 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A213029

a(n) = floor(n/2)^2 - floor(n/3)^2.

0, 0, 1, 0, 3, 3, 5, 5, 12, 7, 16, 16, 20, 20, 33, 24, 39, 39, 45, 45, 64, 51, 72, 72, 80, 80, 105, 88, 115, 115, 125, 125, 156, 135, 168, 168, 180, 180, 217, 192, 231, 231, 245, 245, 288, 259, 304, 304, 320, 320, 369, 336, 387, 387, 405, 405, 460, 423

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,1,3,2,-2,-3,-1,1,1).

FORMULA

a(n) = -a(n-1)+a(n-2)+3*a(n-3)+2*a(n-4)-2*a(n-5)-3*a(n-6)-a(n-7)+a(n-8)+a(n-9).

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

MATHEMATICA

a[n_] := Floor[n/2]^2 - Floor[n/3]^2

Table[a[n], {n, 0, 60}] (* A213029 *)

LinearRecurrence[{-1, 1, 3, 2, -2, -3, -1, 1, 1}, {0, 0, 1, 0, 3, 3, 5, 5, 12}, 60]

CoefficientList[Series[(x^2 + x^3 + 2 x^4 + 3 x^5 + 3 x^6) / (1 + x - x^2 - 3 x^3 - 2 x^4 + 2 x^5 + 3 x^6 + x^7 - x^8 - x^9), {x, 0, 80}], x] (* Vincenzo Librandi, Aug 02 2013 *)

PROG

(Magma) I:=[0, 0, 1, 0, 3, 3, 5, 5, 12]; [n le 9 select I[n] else -Self(n-1)+Self(n-2)+3*Self(n-3)+2*Self(n-4)-2*Self(n-5)-3*Self(n-6)-Self(n-7)+Self(n-8)+Self(n-9): n in [1..60]]; // Vincenzo Librandi, Aug 02 2013

CROSSREFS

Sequence in context: A245144 A279021 A339555 * A348843 A290208 A171710

Adjacent sequences: A213026 A213027 A213028 * A213030 A213031 A213032

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 05 2012

EXTENSIONS

Formula corrected by Vincenzo Librandi, Aug 02 2013

STATUS

approved