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A093485 a(n) = (27*n^2 + 9*n + 2)/2. 3
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A183455 A183340 A195749 * A226633 A156967 A244146
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

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Last modified April 18 04:56 EDT 2024. Contains 371767 sequences. (Running on oeis4.)