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 A027468 9 times the triangular numbers A000217. 25
 0, 9, 27, 54, 90, 135, 189, 252, 324, 405, 495, 594, 702, 819, 945, 1080, 1224, 1377, 1539, 1710, 1890, 2079, 2277, 2484, 2700, 2925, 3159, 3402, 3654, 3915, 4185, 4464, 4752, 5049, 5355, 5670, 5994, 6327, 6669, 7020, 7380, 7749, 8127, 8514, 8910, 9315 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Staggered diagonal of triangular spiral in A051682, between (0,1,11) spoke and (0,8,25) spoke. - Paul Barry, Mar 15 2003 Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-2 fixed points. - Zerinvary Lajos, Oct 15 2006 Number of n permutations (n>=2) of 4 objects u, v, z, x with repetition allowed, containing n-2=0 u's. Example: if n=2 then n-2 =zero (0) u, a(1)=9 because we have vv, zz, xx, vx, xv, zx, xz, vz, zv. A027465 formatted as a triangular array: diagonal: 9, 27, 54, 90, 135, 189, 252, 324, ... . - Zerinvary Lajos, Aug 06 2008 a(n) is also the least weight of self-conjugate partitions having n different parts such that each part is a multiple of 3. - Augustine O. Munagi, Dec 18 2008 Also sequence found by reading the line from 0, in the direction 0, 9, ..., and the same line from 0, in the direction 0, 27, ..., in the square spiral whose vertices are the generalized hendecagonal numbers A195160. Axis perpendicular to A195147 in the same spiral. - Omar E. Pol, Sep 18 2011 Sum of the numbers from 4*n to 5*n. - Wesley Ivan Hurt, Nov 01 2014 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 A. O. Munagi, Pairing conjugate partitions by residue classes, Discrete Math., 308 (2008), 2492-2501. Enrique Navarrete, Daniel Orellana, Finding Prime Numbers as Fixed Points of Sequences, arXiv:1907.10023 [math.NT], 2019. D. Zvonkine, Counting ramified coverings and intersection theory on Hurwitz spaces II (local structure of Hurwitz spaces and combinatorial results), Moscow Mathematical Journal, vol. 7 (2007), no. 1, 135-162. D. Zvonkine, Home Page Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA Numerators of sequence a[ n, n-2 ] in (a[ i, j ])^2 where a[ i, j ] = Binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i a(n) = (9/2)*n*(n+1). a(n) = 9*C(n, 1) + 9*C(n, 2) (binomial transform of (0, 9, 9, 0, 0, .....)). - Paul Barry, Mar 15 2003 G.f.: 9*x/(1-x)^3. a(-1-n) = a(n). a(n) = C(n+1,2)*3^2, n>=0. - Zerinvary Lajos, Aug 06 2008 a(n) = a(n-1) + 9*n (with a(0)=0). - Vincenzo Librandi, Nov 19 2010 a(n) = A060544(n+1) - 1. - Omar E. Pol, Oct 03 2011 a(n) = A218470(9*n+8). - Philippe Deléham, Mar 27 2013 E.g.f.: (9/2)*x*(x+2)*exp(x). - G. C. Greubel, Aug 22 2017 EXAMPLE The first such self-conjugate partitions, corresponding to a(n)=1,2,3,4 are 3+3+3, 6+6+6+3+3+3, 9+9+9+6+6+6+3+3+3, 12+12+12+9+9+9+6+6+6+3+3+3. - Augustine O. Munagi, Dec 18 2008 MAPLE [seq(9*binomial(n, 2), n=1..46)]; # Zerinvary Lajos, Nov 24 2006 seq(binomial(n+1, 2)*3^2, n=0..22); # Zerinvary Lajos, Aug 06 2008 MATHEMATICA s = 0; lst = {}; Do[s += n + 0; AppendTo[lst, s*3], {n, 0, 160, 3}] ; lst (* Zerinvary Lajos, Jul 10 2009 *) Table[(9/2)*n*(n+1), {n, 0, 50}] (* G. C. Greubel, Aug 22 2017 *) PROG (PARI) a(n)=9*n*(n+1)/2 (MAGMA) [9*n*(n+1)/2: n in [0..50]]; // Vincenzo Librandi, Dec 29 2012 CROSSREFS Third diagonal of A027465. Cf. A033996, A049598, A000459, A059073, A028895, A046092, A045943, A002378, A028896, A024966, A008585, A134171, A038764, A080855, A283394. Sequence in context: A020306 A069068 A051412 * A158926 A112524 A254622 Adjacent sequences:  A027465 A027466 A027467 * A027469 A027470 A027471 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Patrick De Geest, Oct 15 1999 STATUS approved

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Last modified November 11 15:46 EST 2019. Contains 329018 sequences. (Running on oeis4.)