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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 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

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