A093485 a(n) = (27*n^2 + 9*n + 2)/2.

1, 19, 64, 136, 235, 361, 514, 694, 901, 1135, 1396, 1684, 1999, 2341, 2710, 3106, 3529, 3979, 4456, 4960, 5491, 6049, 6634, 7246, 7885, 8551, 9244, 9964, 10711, 11485, 12286, 13114, 13969, 14851, 15760, 16696, 17659, 18649, 19666, 20710, 21781

Offset

0,2

Comments

Dodecahedral gnomon numbers: first differences of dodecahedral numbers.

The sequence is related to other gnomon numbers of polyhedra, known by other more familiar names: triangular numbers (tetrahedral gnomon numbers), hexagonal numbers (cubic gnomon numbers), square pyramidal numbers (octahedral gnomon numbers).

A124388 = first differences; second differences = 27. - Reinhard Zumkeller, Oct 30 2006

Sums of the triangular numbers from A000217(3*n-1) to A000217(3*n+1), with A000217(-1) = 0. - Bruno Berselli, Sep 04 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = (n+1)*(3*(n+1)-1)*(3*(n+1)-2)/2-n*(3*n-1)*(3*n-2)/2.

G.f.: (1 + 16*x + 10*x^2)/(1 - x)^3. - Colin Barker, Mar 28 2012

Example

a(1) = 19 because (1+1)*(3*(1+1)-1)*(3*(1+1)-2)/2-1*(3*1-1)*(3*1-2)/2 = 2*(6-1)*(6-2)/2 - 1*(3-1)*(3-2)/2 = 20-1 = 19.

Prog

(Magma) [(27*n^2 + 9*n + 2)/2 : n in [0..50]]; // Vincenzo Librandi, Oct 08 2011
(Haskell)
a093485 n = (9 * n * (3 * n + 1) + 2) `div` 2
-- Reinhard Zumkeller, Jun 16 2013
(PARI) a(n)=(27*n^2+9*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A000330, A003215, A005901, A006656.

Sequence in context: A183455 A183340 A195749 * A226633 A156967 A244146

Adjacent sequences: A093482 A093483 A093484 * A093486 A093487 A093488

Keyword

nonn,easy

Author

Michael Joseph Halm, May 13 2004

Extensions

New definition from Ralf Stephan, Dec 01 2004

Name corrected and initial term added by Arkadiusz Wesolowski, Aug 15 2011

Status

approved