A123228 Sum of the n-th powers of the roots of the polynomial x^6 + 14x^5 + 87x^4 + 148x^3 + 87x^2 + 14x + 1.

6, -14, 22, 466, -6714, 51346, -205418, -638414, 19787526, -195455054, 1126500502, -1636604654, -47878102074, 662684162386, -4965254864618, 19072814136946, 71067700116486, -1976406503675534, 19086772122105622, -107375947452919214, 128777308208472006, 4884916184617735186

Offset

0,1

Links

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (-13,-74,-74,-13,-1).

Formula

G.f.: 2*(7*x^4+80*x^3+142*x^2+32*x+3)/((x+1)*(x^4+12*x^3+62*x^2+12*x+1)).

Maple

Newt:=proc(f) local t1, t2, t3, t4; t1:=f; t2:=diff(f, x); t3:=expand(x^degree(t1, x)*subs(x=1/x, t1)); t4:=expand(x^degree(t2, x)*subs(x=1/x, t2)); factor(t4/t3); end;
t1:=1+14*x+87*x^2+148*x^3+87*x^4+14*x^5+x^6; Newt(t1); series(t1, x, 50);

Prog

(PARI) polsym(x^6 + 14*x^5 + 87*x^4 + 148*x^3 + 87*x^2 + 14*x + 1, 30) \\ Charles R Greathouse IV, Jul 20 2016

Crossrefs

This polynomial arises in A001496. Cf. A123259.

Sequence in context: A190522 A079797 A093380 * A015832 A190753 A190740

Adjacent sequences: A123225 A123226 A123227 * A123229 A123230 A123231

Keyword

sign,easy

Author

N. J. A. Sloane, Nov 12 2006

Status

approved