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A014126 Number of partitions of 2*n into at most 4 parts.
(Formerly N0523)
7
1, 2, 5, 9, 15, 23, 34, 47, 64, 84, 108, 136, 169, 206, 249, 297, 351, 411, 478, 551, 632, 720, 816, 920, 1033, 1154, 1285, 1425, 1575, 1735, 1906, 2087, 2280, 2484, 2700, 2928, 3169, 3422, 3689, 3969, 4263, 4571, 4894, 5231, 5584, 5952, 6336, 6736, 7153 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Bisection of A001400.

Molien series for 4-dimensional group of structure S_4 X C_2 and order 48, arising from to complete weight enumerators of even trace-Hermitian self-dual additive codes over GF(4) containing the all-ones vector.

Partial sums of A156040. - Bob Selcoe, Feb 08 2014

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

L. Colmenarejo, Combinatorics on several families of Kronecker coefficients related to plane partitions, arXiv:1604.00803 [math.CO], 2016. See Table 1 p. 5.

H. R. Henze, C. M. Blair, The number of structurally isomeric Hydrocarbons of the Ethylene Series, J. Amer. Chem. Soc., 55 (2) (1933), 680-686.

H. R. Henze, C. M. Blair, The number of structurally isomeric Hydrocarbons of the Ethylene Series, J. Amer. Chem. Soc., 55 (2) (1933), 680-685. (Annotated scanned copy)

G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,0,2,-1).

FORMULA

G.f.: (1+x^2)/((1-x)^2*(1-x^2)*(1-x^3)). - James A. Sellers

a(n) = (1/72) * (4*n^3 + 30*n^2 + 72*n + 55 + 8*A049347(n) + 9*(-1)^n ). - Ralf Stephan, Aug 15 2013

MAPLE

with(combstruct): seq(count(Partition((2*n+4)), size=4), n=0..50); # Zerinvary Lajos, Mar 28 2008

MATHEMATICA

CoefficientList[Series[(1 + x^2) / ((1 - x)^2 (1 - x^2) (1 - x^3)), {x, 0, 100}], x] (* Vincenzo Librandi, Aug 15 2013 *)

LinearRecurrence[{2, 0, -1, -1, 0, 2, -1}, {1, 2, 5, 9, 15, 23, 34}, 50] (* Harvey P. Dale, Aug 31 2015 *)

PROG

(PARI) a(n)=(4*n^3+30*n^2+72*n+55+8*[1, -1, 0][(n%3)+1]+9*(-1)^n)/72

CROSSREFS

Cf. A092498, A014125, A000631, A001400.

Sequence in context: A308265 A218914 A047809 * A019450 A098169 A055610

Adjacent sequences:  A014123 A014124 A014125 * A014127 A014128 A014129

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 22 00:39 EDT 2021. Contains 345367 sequences. (Running on oeis4.)