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A016138
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Expansion of 1/((1-3x)(1-7x)).
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2
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1, 10, 79, 580, 4141, 29230, 205339, 1439560, 10083481, 70604050, 494287399, 3460188940, 24221854021, 169554572470, 1186886790259, 8308221880720, 58157596211761, 407103302622490, 2849723505777919
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (10,-21).
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FORMULA
| (7^(n+1)-3^(n+1))/4 - Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005
((5+sqrt4)^n-(5-sqrt4)^n)/4 in Fibonacci form. Offset 1. a(3)=79. [From Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008]
a(n)=10*a(n-1)-21*a(n-2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 01 2009]
G.f.: x/(1-10*x+21*x^2); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
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MATHEMATICA
| Join[{a=1, b=10}, Table[c=10*b-21*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 10, 21) for n in xrange(1, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
(MAGMA) [(7^(n+1)-3^(n+1))/4: n in [0..20]]; // Vincenzo Librandi, Oct 09 2011
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CROSSREFS
| Sequence in context: A160655 A006469 A081905 * A006329 A077245 A036732
Adjacent sequences: A016135 A016136 A016137 * A016139 A016140 A016141
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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