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A155622
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a(n) = 11^n - 2^n + 1.
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12
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1, 10, 118, 1324, 14626, 161020, 1771498, 19487044, 214358626, 2357947180, 25937423578, 285311668564, 3138428372626, 34522712135740, 379749833566858, 4177248169382884, 45949729863506626, 505447028499162700
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OFFSET
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0,2
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COMMENTS
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In general: r^n - s^n + 1 = (r+s)*a(n-1)-(r*s)*a(n-2)+(r-1)*(s-1). - Vincenzo Librandi, Jul 21 2010
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LINKS
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Table of n, a(n) for n=0..17.
Index entries for linear recurrences with constant coefficients, signature (14,-35,22).
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FORMULA
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G.f.: 1/(1 - 11*x) - 1/(1 - 2*x) + 1/(1-x).
E.g.f.: exp(11*x) - exp(2*x) + exp(x).
a(n) = 13*a(n-1) - 22*a(n-2) + 10 for n>1, a(0)=1, a(1)=10. - Vincenzo Librandi, Jul 21 2010
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MATHEMATICA
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Table[11^n - 2^n + 1, {n, 0, 20}] (* or *) LinearRecurrence[{14, -35, 22}, {1, 10, 118}, 20] (* Harvey P. Dale, Oct 21 2013 *)
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PROG
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(PARI) a(n)=11^n-2^n+1 \\ Charles R Greathouse IV, Jun 11 2015
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CROSSREFS
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Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601.
Sequence in context: A024129 A262970 A309582 * A307695 A218501 A293987
Adjacent sequences: A155619 A155620 A155621 * A155623 A155624 A155625
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian, Jan 29 2009
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STATUS
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approved
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