A153266 a(n) = -4*a(n-3) + 11*a(n-2) - a(n-1), a(0) = 13, a(1) = -19, a(2) = 162.

13, -19, 162, -423, 2281, -7582, 34365, -126891, 535234, -2068495, 8463633, -33358014, 134731957, -535524643, 2151008226, -8580707127, 34383896185, -137375707486, 549921394029, -2198589761115, 8797227925378

Offset: 0

Author

Creighton Dement, Jan 02 2009

Keywords

• easy
• sign

Comments

a(n) + A153267(n) = 4*A001519(n) (apart from initial terms). The generating floretion Z = X*Y with X = 1.5'i + 0.5i' + .25(ii + jj + kk + ee) and Y = 0.5'i + 1.5i' + .25(ii + jj + kk + ee)

Examples

			a(4) = -1*(-423) + 11*162 - 4*(-19) = 2281
		

Links

• Index entries for linear recurrences with constant coefficients, signature (-1, 11, -4).

Crossrefs

A153267, A153265, A001519

Formula

a(n) = 2*(-4)^n + (-2/5*sqrt(5)-1)*(3/2+1/2*sqrt(5))^n + (2/5*sqrt(5)-1)*(3/2-1/2*sqrt(5))^n

a(n)=A001519(n+3)+8*(-4)^n. G.f.: (13-6x)/((1+4x)(1-3x+x^2)). [From R. J. Mathar, Jan 05 2009]