A008504 10-dimensional centered tetrahedral numbers.

1, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960, 352716, 705431, 1352066, 2496066, 4457036, 7724795, 13033527, 21461804, 34565466, 54551718, 84504355, 128671764, 192831288, 284745682

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Formula

G.f.: (1-x^11)/(1-x)^12 = (1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)/(1-x)^11.

a(n) = 1 + 11*n*(n+1)*(n^8 +4*n^7 +416*n^6 +1234*n^5 +28019*n^4 +53986*n^3 +395644*n^2 +368856*n +966240)/3628800. - Bruno Berselli, Mar 22 2012

Maple

seq(binomial(n+11, 11)-binomial(n, 11), n=0..30); # G. C. Greubel, Nov 09 2019

Mathematica

Table[Binomial[n + 11, 11] - Binomial[n, 11], {n, 0, 23}] (* Bruno Berselli, Mar 22 2012 *)
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {1, 12, 78, 364, 1365, 4368, 12376, 31824, 75582, 167960, 352716}, 30] (* Harvey P. Dale, Dec 25 2023 *)

Prog

(PARI) vector(31, n, b=binomial; b(n+10, 11) - b(n-1, 11) ) \\ G. C. Greubel, Nov 09 2019
(Magma) B:=Binomial; [B(n+11, 11)-B(n, 11): n in [0..30]]; // G. C. Greubel, Nov 09 2019
(Sage) b=binomial; [b(n+11, 11)-b(n, 11) for n in (0..30)] # G. C. Greubel, Nov 09 2019
(GAP) B:=Binomial;; List([0..30], n-> B(n+11, 11)-B(n, 11) ); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A304503 A268793 A162629 * A008494 A001288 A290894

Adjacent sequences: A008501 A008502 A008503 * A008505 A008506 A008507

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved