Search: id:A038764
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%I A038764
%S A038764 1,7,22,46,79,121,172,232,301,379,466,562,667,781,904,1036,1177,1327,
%T A038764 1486,1654,1831,2017,2212,2416,2629,2851,3082,3322,3571,3829,4096,4372,
%U A038764 4657,4951,5254,5566,5887,6217,6556,6904,7261,7627,8002,8386,8779,9181
%N A038764 a(n)=C(n,0)+6C(n,1)+9C(n,2).
%C A038764 Coefficients of x^2 of certain rook polynomials (for n>=1; see p. 18 
               of the Riordan paper). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 08 2004
%C A038764 a(n) is also the least weight of self-conjugate partitions having n+1 
               different parts such that each part is congruent to 1 modulo 3. [From 
               Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
%D A038764 S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing 
               hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.
%D A038764 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A038764 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]
%F A038764 Binomial transform of (1, 6, 9, 0, 0, 0, .....). a(n)=(9n^2+3n+2)/2. 
               G.f.(1+4x+4x^2)/(1-x)^3. - Paul Barry (pbarry(AT)wit.ie), Mar 15 
               2003
%F A038764 a(n)=9*n+a(n-1)-12 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 10 2009]
%e A038764 The first such self-conjugate partitions, corresponding to a(n)=0,1,2,
               3, are 1, 4+3, 7+4+4+4+3, 10+7+7+7+4+4+4+3. [From Augustine O. Munagi 
               (amunagi(AT)yahoo.com), Dec 18 2008]
%e A038764 For n=2, a(2)=9*2+1-12=7; n=3, a(3()=9*3+7-12=22; n=4, a(4)=9*4+22-12=46 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 10 2009]
%Y A038764 Reflection of A060544 in A081272.
%Y A038764 Second column of A024462. Also = A064641(n+1, 2).
%Y A038764 Shallow diagonal of triangular spiral in A051682.
%Y A038764 Cf. A027468, A080855 [From Augustine O. Munagi (amunagi(AT)yahoo.com), 
               Dec 18 2008]
%Y A038764 Sequence in context: A033954 A159227 A081274 this_sequence A132438 A010001 
               A014073
%Y A038764 Adjacent sequences: A038761 A038762 A038763 this_sequence A038765 A038766 
               A038767
%K A038764 nonn,easy
%O A038764 0,2
%A A038764 N. J. A. Sloane (njas(AT)research.att.com), May 03 2000
%E A038764 More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000

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