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A059251 A sequence related to numeric partitions and Fermat Coefficients. 0
1, 1, 5, 15, 44, 99, 217, 429, 811, 1430, 2438, 3978, 6312, 9690, 14550, 21318, 30669, 43263, 60115, 82225, 111044, 148005, 195143, 254475, 328759, 420732, 534076, 672452, 840656, 1043460, 1287036, 1577532, 1922745, 2330445, 2810385, 3372291 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The sequences m1^8, m2^4 and 6*m4^2 correspond to eight elements of a finite group of order eight belonging to the appropriate partition class.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

Let m1^8 = A000580, m2^4 = 1 0 4 0 10 0 20 ... and let m4^2 = 1 0 0 0 2 0 0 0 3 0 0 0 4 ... Then a(n) = (1/8)*(m1^8 + m2^4 + 6*m4^2).

Empirical g.f.: x*(1 - 3*x + 5*x^2 + 3*x^3 - 4*x^4 + 3*x^5 + 5*x^6 - 3*x^7 + x^8) / ((1 - x)^8*(1 + x)^4*(1 + x^2)^2). - Colin Barker, Mar 30 2017

EXAMPLE

a(5)= 44 because (1/8)*( 330 + 10 + 12) = 352/8; a(9)= 811 because (1/8)*(6435 + 35 + 18) = 6488/8.

CROSSREFS

Cf. A000041, A000292, A000580, A000973, A058936.

Sequence in context: A005665 A025471 A064453 * A295179 A274020 A109952

Adjacent sequences:  A059248 A059249 A059250 * A059252 A059253 A059254

KEYWORD

easy,nonn

AUTHOR

Alford Arnold, Jan 22 2001

EXTENSIONS

More terms from David Wasserman, Jun 07 2002

STATUS

approved

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Last modified October 19 20:58 EDT 2019. Contains 328224 sequences. (Running on oeis4.)