A264443 a(n) = n*(n + 5)*(n + 10)/6.

0, 11, 28, 52, 84, 125, 176, 238, 312, 399, 500, 616, 748, 897, 1064, 1250, 1456, 1683, 1932, 2204, 2500, 2821, 3168, 3542, 3944, 4375, 4836, 5328, 5852, 6409, 7000, 7626, 8288, 8987, 9724, 10500, 11316, 12173, 13072, 14014, 15000

Offset

0,2

Comments

It is well-known, and easy to prove, that the product of 3 consecutive integers n*(n + 1)*(n + 2) is divisible by 6. It can be shown that the product of 3 integers in arithmetic progression n*(n + r)*(n + 2*r) is divisible by 6 if and only if r is not divisible by 2 or 3 (see A007310 for these numbers). This is the case r = 5.

Links

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

O.g.f.: x*(6*x^2 - 16*x + 11)/(1 - x)^4.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3. - Vincenzo Librandi, Nov 16 2015

Maple

seq( n*(n + 5)*(n + 10)/6, n = 1..40 );

Mathematica

Table[n (n + 5) (n + 10)/6, {n, 0, 40}] (* Vincenzo Librandi, Nov 16 2015 *)

Prog

(PARI) vector(100, n, n--; n*(n+5)*(n+10)/6) \\ Altug Alkan, Nov 15 2015
(Magma) [n*(n+5)*(n+10)/6: n in [0..40]]; // Vincenzo Librandi, Nov 16 2015

Crossrefs

Cf. A007310, A264444, A264445, A264446, A264447, A264448, A264449, A264450.

Sequence in context: A061952 A336335 A140677 * A364893 A349660 A242941

Adjacent sequences: A264440 A264441 A264442 * A264444 A264445 A264446

Keyword

nonn,easy

Author

Peter Bala, Nov 13 2015

Status

approved