A016157 - OEIS

A016157

Expansion of g.f. 1/((1-4*x)*(1-10*x)).

1, 14, 156, 1624, 16496, 165984, 1663936, 16655744, 166622976, 1666491904, 16665967616, 166663870464, 1666655481856, 16666621927424, 166666487709696, 1666665950838784, 16666663803355136, 166666655213420544

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (14,-40).

FORMULA

a(n) = ((7+sqrt(9))^(n+1) - (7-sqrt(9))^(n+1))/6. - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009

From Vincenzo Librandi, Mar 18 2011: (Start)

a(n) = 14*a(n-1) - 40*a(n-2), n >= 2.

a(n) = 10*a(n-1) + 4^n = 4*a(n-1) + 10^n, n >= 1. (End)

a(n) = (5*10^n - 2*4^n)/3. - Bruno Berselli, Mar 19 2011

E.g.f.: exp(4*x)*(5*exp(6*x) - 2)/3. - Stefano Spezia, Sep 30 2023

MATHEMATICA

Join[{a=1, b=14}, Table[c=14*b-40*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)

CROSSREFS

Sequence in context: A154347 A001707 A078999 * A238770 A199703 A144166

Adjacent sequences: A016154 A016155 A016156 * A016158 A016159 A016160

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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