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A012855
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Take every 5th term of Padovan sequence A000931.
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7
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0, 1, 1, 1, 2, 7, 28, 114, 465, 1897, 7739, 31572, 128801, 525456, 2143648, 8745217, 35676949, 145547525, 593775046, 2422362079, 9882257736, 40315615410, 164471408185, 670976837021, 2737314167775, 11167134898976
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OFFSET
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0,5
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LINKS
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Table of n, a(n) for n=0..25.
Index to sequences with linear recurrences with constant coefficients, signature (5,-4,1).
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FORMULA
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a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
G.f. (4x^2-x)/(x^3-4x^2+5x-1). For n>2, a(n) = 1 + sum(k=0, n-3, A012814(k)). - Ralf Stephan, Jan 15 2004
a(0)=0, a(1)=1, a(2)=1, a(n)=5*a(n-1)-4*a(n-2)+a(n-3). - Harvey P. Dale, Mar 28 2013
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MAPLE
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A012855 := proc(n, A, B, C) option remember; if n = 0 then A elif n = 1 then B elif n = 2 then C else 5*procname(n-1, A, B, C)-4*procname(n-2, A, B, C)+procname(n-3, A, B, C); fi; end; [ seq(A012855(i, 0, 1, 1), i = 0..40) ];
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MATHEMATICA
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CoefficientList[Series[(4x^2-x)/(x^3-4x^2+5x-1), {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -4, 1}, {0, 1, 1}, 40] (* Harvey P. Dale, Mar 28 2013 *)
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CROSSREFS
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Sequence in context: A099488 A068944 A215143 * A224066 A150646 A128611
Adjacent sequences: A012852 A012853 A012854 * A012856 A012857 A012858
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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