A059251 A sequence related to numeric partitions and Fermat Coefficients.

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

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