0,2

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]

Except for the first term, a(n)=9*n+a(n-1), (with a(1)=9) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]

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]

Index entries for two-way infinite sequences

D. Zvonkine, Home Page

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)=9*n+a(n-1)-9 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

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]

For n=2, a(2)=9*2+0-9=9; n=3, a(3)=9*3+9-9=27; n=4, a(4)=9*4+27-9=54 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 12 2009]

[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]

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]

(PARI) a(n)=9*n*(n+1)/2

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 this_sequence A158926 A112524 A153237

Adjacent sequences: A027465 A027466 A027467 this_sequence A027469 A027470 A027471

nonn,easy,new

Olivier Gerard (olivier.gerard(AT)gmail.com)

More terms from Patrick De Geest (pdg(AT)worldofnumbers.com), Oct 15 1999.