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

Author

Alford Arnold, Jan 22 2001

Keywords

• easy
• nonn

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.

Examples

			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.

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

Extensions

More terms from David Wasserman, Jun 07 2002