A143465 A McMullen transform involving x->x+1/x of Lehmer's polynomial gives the polynomial used to get this expansion sequence: p(x)=1 + x + 10 x^2 + 8 x^3 + 44 x^4 + 28 x^5 + 113 x^6 + 57 x^7 + 191 x^8 + 79 x^9 + 227 x^10 + 79 x^11 + 191 x^12 + 57 x^13 + 113 x^14 + 28 x^15 + 44 x^16 + 8 x^17 + 10 x^18 + x^19 + x^20.

1, -1, -9, 11, 43, -65, -142, 272, 351, -897, -636, 2458, 618, -5746, 1125, 11522, -8822, -19299, 34019, 23687, -107090, -3953, 305278, -106133, -814418, 505401, 2042163, -1769399, -4753130, 5499052, 9967351

Offset

1,3

Links

Table of n, a(n) for n=1..31.

Formula

q(x)=x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1; p(x)=x^10*q(x+1/x); p(x)=1 + x + 10 x^2 + 8 x^3 + 44 x^4 + 28 x^5 + 113 x^6 + 57 x^7 + 191 x^8 + 79 x^9 + 227 x^10 + 79 x^11 + 191 x^12 + 57 x^13 + 113 x^14 + 28 x^15 + 44 x^16 + 8 x^17 + 10 x^18 + x^19 + x^20; a(n)=Coefficient_Expansion(x^20*p(1/x)).

Mathematica

f[x_] = x^10 + x^9 - x^7 - x^6 - x^5 - x^4 - x^3 + x + 1; h[x_] = ExpandAll[x^10*f[x + 1/x]]; g[x] = ExpandAll[x^20*h[1/x]]; a = Table[SeriesCoefficient[ Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}]

Crossrefs

Sequence in context: A129399 A145790 A345109 * A201999 A195309 A242507

Adjacent sequences: A143462 A143463 A143464 * A143466 A143467 A143468

Keyword

uned,sign

Author

Roger L. Bagula and Gary W. Adamson, Oct 24 2008

Status

approved