A061553 Sum of absolute values of coefficients of expansion of (1-x)(1-x^2)(1-x^3)...(1-x^n).

1, 2, 4, 6, 8, 12, 16, 20, 28, 36, 44, 54, 72, 92, 104, 138, 176, 212, 268, 332, 416, 508, 628, 776, 968, 1192, 1480, 1836, 2288, 2812, 3472, 4292, 5312, 6572, 8120, 10028, 12388, 15300, 18860, 23276, 28740, 35468, 43732, 53954, 66540, 82016, 101044

Offset

0,2

Comments

a(n) >= A160089(n) with equality only for n=0. - Michel Marcus, Jun 12 2013

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

a(n) := |c(n, 0)| + |c(n, 1)| + ... + |c(n, n(n+1)/2)| where c(n, j) are the coefficients of the polynomial P(n, x) := (1-x)(1-x^2)(1-x^3)...(1-x^n)

Example

a(1) = 1+1 = 2; a(4) = Length(P(4,x)) = Length(1 - x - x^2 + 2x^5 - x^8 - x^9 + x^10) = 1+1+1+2+1+1+1 = 8

Prog

(PARI) a(n) = {pol = prod(i=1, n, 1-x^i); return (sum(i=0, poldegree(pol), abs(polcoeff(pol, i)))); } \\ Michel Marcus, Jun 12 2013

Crossrefs

Cf. A160089, A231599.

Sequence in context: A097921 A185976 A117146 * A138934 A008764 A228354

Adjacent sequences: A061550 A061551 A061552 * A061554 A061555 A061556

Keyword

nonn

Author

Steffen Eckmann (steffen.eckmann(AT)eon.com), May 17 2001

Extensions

a(0)=1 prepended by Seiichi Manyama, May 03 2018

Status

approved