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A027468
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9 times triangular numbers A000217.
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21
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| Staggered diagonal of triangular spiral in A051682, between (0,1,11) spoke and (0,8,25) spoke. - Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
Number of permutations of n distinct letters (ABCD...) each of which appears thrice with n-2 fixed points. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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, ... [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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. [From Augustine O. Munagi (amunagi(AT)yahoo.com), 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
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REFERENCES
| Zvonkine D., 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.
A. O. Munagi, Pairing conjugate partitions by residue classes, Discrete Math., 308 (2008), 2492--2501. [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
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LINKS
| Index entries for two-way infinite sequences
D. Zvonkine, Home Page
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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)=9C(n, 1)+9C(n, 2) (binomial transform of (0, 9, 9, 0, 0, .....)). - Paul Barry (pbarry(AT)wit.ie), Mar 15 2003
G.f.: 9x/(1-x)^3. a(-1-n)=a(n).
a(n)=C(n+1,2)*3^2, n>=0. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
a(n)=a(n-1)+9*n (with a(0)=0) [From Vincenzo Librandi, Nov 19 2010]
a(n) = A060544(n+1) - 1. - Omar E. Pol, Oct 03 2011
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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 [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
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MAPLE
| [seq(9*binomial(n, 2), n=1..46)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 24 2006
seq(binomial(n+1, 2)*3^2, n=0..22); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
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MATHEMATICA
| s = 0; lst = {}; Do[s += n + 0; AppendTo[lst, s*3], {n, 0, 160, 3}] ; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 10 2009]
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PROG
| (PARI) a(n)=9*n*(n+1)/2
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CROSSREFS
| Third diagonal of A027465. Cf. A033996, A049598.
Cf. A059072, A059073.
Cf. A028895, A046092, A045943, A002378, A028896, A024966, A033996.
A008585, A027465, A134171 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 06 2008]
Cf. A038764, A080855 [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
Sequence in context: A020306 A069068 A051412 * A158926 A112524 A153237
Adjacent sequences: A027465 A027466 A027467 * A027469 A027470 A027471
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Oct 15 1999.
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