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A234041 a(n) = binomial(n+2,2)*gcd(n,3)/3, n >= 0. 3
1, 1, 2, 10, 5, 7, 28, 12, 15, 55, 22, 26, 91, 35, 40, 136, 51, 57, 190, 70, 77, 253, 92, 100, 325, 117, 126, 406, 145, 155, 496, 176, 187, 595, 210, 222, 703, 247, 260, 820, 287, 301, 946, 330, 345, 1081, 376, 392, 1225, 425, 442, 1378, 477, 495, 1540, 532 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Apart from the first term, this is the same as A027626. [Bruno Berselli, Feb 24 2014]

This is the sequence of the fourth column of the triangle A107711.

a(n) is the numerator of (n+1)*(n+2)/6. - Altug Alkan, Apr 19 2018

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

FORMULA

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

a(n) = A107711(n+3,3) for n >= 0.

a(n) = (2+(-1)^(n+floor((n+1)/3)))*(n+1)*(n+2)/6. [Bruno Berselli, Feb 24 2014]

EXAMPLE

a(6) = binomial(8,2) = 28 (example for n == 0 (mod 3)),

a(7) = binomial(9,2)/3 = 3*4 = 12 (example for n == 1 (mod 3)),

a(8) = binomial(10,2)/3 = 5*3 = 15 (example for n == 2 (mod 3)).

MATHEMATICA

Table[Binomial[n + 2, 2] GCD[n + 3, 3]/3, {n, 0, 60}] (* Bruno Berselli, Feb 24 2014 *)

CoefficientList[Series[(1 + x + 2 x^2 + 7 x^3 + 2 x^4 + x^5 + x^6)/(1 - x^3)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Feb 26 2014 *)

PROG

(PARI) a(n) = numerator((n+1)*(n+2)/6); \\ Altug Alkan, Apr 19 2018

CROSSREFS

Cf. A027626, A107711, A026741 (third column of A107711), A109007 (gcd(n,3)).

Sequence in context: A038216 A213603 A145911 * A027626 A096668 A114232

Adjacent sequences:  A234038 A234039 A234040 * A234042 A234043 A234044

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 24 2014

STATUS

approved

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Last modified May 17 05:06 EDT 2021. Contains 343964 sequences. (Running on oeis4.)