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A274099 Number of partitions of n*(n-1)/2 into at most four parts. 3
1, 1, 3, 9, 23, 54, 120, 249, 478, 864, 1495, 2484, 3969, 6136, 9234, 13561, 19464, 27378, 37845, 51488, 69012, 91260, 119239, 154078, 197026, 249535, 313290, 390144, 482120, 591519, 720954, 873264, 1051513, 1259130, 1499950, 1778097, 2097984, 2464489 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

FORMULA

Coefficient of x^(n*(n-1)/2) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

Empirical g.f.: (1 -5*x +15*x^2 -30*x^3 +54*x^4 -77*x^5 +109*x^6 -128*x^7 +150*x^8 -148*x^9 +150*x^10 -128*x^11 +109*x^12 -77*x^13 +54*x^14 -30*x^15 +15*x^16 -5*x^17 +x^18) / ((1 -x)^7*(1 +x^2)^3*(1 +x +x^2)*(1 +x^4)). - Colin Barker, Jun 12 2016

MATHEMATICA

Length[IntegerPartitions[#, 4]]&/@Accumulate[Range[0, 40]] (* Harvey P. Dale, Jul 08 2022 *)

PROG

(PARI)

\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).

b(n) = round(real((68+36*(-1)^n+18*((-I)^n+I^n)+(16*exp(-2/3*I*n*Pi)*(1+I*sqrt(3)+2*exp((4*I*n*Pi)/3)))/(1+(-1)^(1/3))+59*(1+n)+9*(-1)^n*(1+n)+18*(1+n)*(2+n)+2*(1+n)*(2+n)*(3+n))/288))

vector(50, n, b(n*(n-1)/2)) \\ Colin Barker, Jun 12 2016

CROSSREFS

A subsequence of A001400.  Cf. A274100.

Sequence in context: A244331 A183155 A305168 * A147126 A147212 A341029

Adjacent sequences:  A274096 A274097 A274098 * A274100 A274101 A274102

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 11 2016

EXTENSIONS

More terms from Colin Barker, Jun 12 2016

STATUS

approved

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Last modified October 6 23:36 EDT 2022. Contains 357270 sequences. (Running on oeis4.)