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A038764
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a(n)=C(n,0)+6C(n,1)+9C(n,2).
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9
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1, 7, 22, 46, 79, 121, 172, 232, 301, 379, 466, 562, 667, 781, 904, 1036, 1177, 1327, 1486, 1654, 1831, 2017, 2212, 2416, 2629, 2851, 3082, 3322, 3571, 3829, 4096, 4372, 4657, 4951, 5254, 5566, 5887, 6217, 6556, 6904, 7261, 7627, 8002, 8386, 8779, 9181
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
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]
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REFERENCES
| S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.
J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
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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FORMULA
| 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
a(n)=a(n-1)+3(3*n-1), (with a(0)=1) [From Vincenzo Librandi, Nov 17 2010]
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EXAMPLE
| 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]
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CROSSREFS
| Reflection of A060544 in A081272.
Second column of A024462. Also = A064641(n+1, 2).
Shallow diagonal of triangular spiral in A051682.
Cf. A027468, A080855 [From Augustine O. Munagi (amunagi(AT)yahoo.com), Dec 18 2008]
Sequence in context: A033954 A159227 A081274 * A132438 A010001 A197059
Adjacent sequences: A038761 A038762 A038763 * A038765 A038766 A038767
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 03 2000
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), May 03 2000
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