A006323 4-dimensional analog of centered polygonal numbers.

1, 10, 41, 115, 260, 511, 910, 1506, 2355, 3520, 5071, 7085, 9646, 12845, 16780, 21556, 27285, 34086, 42085, 51415, 62216, 74635, 88826, 104950, 123175, 143676, 166635, 192241, 220690, 252185, 286936, 325160, 367081, 412930

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = 7*C(n + 2, 4) + C(n + 1, 2).

G.f.: x*(-1-x^2-5*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009; adapted to the offset by Vincenzo Librandi, Sep 06 2013

Sum_{n>=1} 1/a(n) = 30 + 4*sqrt(21/5)*Pi*tan(sqrt(15/7)*Pi/2). - Amiram Eldar, Aug 23 2022

Mathematica

CoefficientList[Series[(-1 - x^2 - 5 x) / (x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 06 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 41, 115, 260}, 40] (* Harvey P. Dale, Dec 27 2022 *)

Prog

(PARI) a(n) = 7*binomial(n + 2, 4) + binomial(n + 1, 2); \\ Michel Marcus, Sep 05 2013
(Magma) [7*Binomial(n+2, 4)+Binomial(n+1, 2): n in [1..40]]; // Vincenzo Librandi, Sep 06 2013

Crossrefs

Sequence in context: A022278 A246972 A266396 * A178073 A102784 A294604

Adjacent sequences: A006320 A006321 A006322 * A006324 A006325 A006326

Keyword

nonn,easy

Author

Albert Rich (Albert_Rich(AT)msn.com)

Status

approved