A264444 a(n) = n*(n + 7)*(n + 14)/6.

0, 20, 48, 85, 132, 190, 260, 343, 440, 552, 680, 825, 988, 1170, 1372, 1595, 1840, 2108, 2400, 2717, 3060, 3430, 3828, 4255, 4712, 5200, 5720, 6273, 6860, 7482, 8140, 8835, 9568, 10340, 11152, 12005, 12900, 13838, 14820, 15847, 16920

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 = 7.

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*(13*x^2 - 32*x + 20)/(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 + 7)*(n + 14)/6, n = 0..40 );

Mathematica

Table[n (n + 7) (n + 14)/6, {n, 0, 40}] (* Vincenzo Librandi, Nov 16 2015 *)

Prog

(PARI) vector(100, n, n--; n*(n+7)*(n+14)/6) \\ Altug Alkan, Nov 15 2015
(Magma) [n*(n+7)*(n+14)/6: n in [0..40]]; // Vincenzo Librandi, Nov 16 2015

Crossrefs

Cf. A007310, A264443, A264445, A264446, A264447, A264448, A264449, A264450.

Sequence in context: A135286 A338235 A177725 * A053245 A115882 A303295

Adjacent sequences: A264441 A264442 A264443 * A264445 A264446 A264447

Keyword

nonn,easy

Author

Peter Bala, Nov 13 2015

Status

approved