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A062544
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n plus sum of previous three terms.
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5
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0, 1, 3, 7, 15, 30, 58, 110, 206, 383, 709, 1309, 2413, 4444, 8180, 15052, 27692, 50941, 93703, 172355, 317019, 583098, 1072494, 1972634, 3628250, 6673403, 12274313, 22575993, 41523737, 76374072, 140473832, 258371672, 475219608
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OFFSET
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0,3
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COMMENTS
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It appears that this is the number of nonempty subsets of {1,2,...,n} with no gap of length greater than 3 (a set S has a gap of length d if a and b are in S but no x with a<x<b is in S, where b-a=d). See A119407 for the corresponding problem for gaps of length 4. - John W. Layman, Nov 02 2011
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LINKS
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Harry J. Smith, Table of n, a(n) for n=0,...,300
Index to sequences with linear recurrences with constant coefficients, signature (3, -2, 0, -1, 1).
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FORMULA
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a(n) = +3*a(n-1) -2*a(n-2) -1*a(n-4) +1*a(n-5) [Joerg Arndt, Apr 2 2011]
a(n) =n+a(n-1)+a(n-2)+a(n-3) =(A001590(n+4)-n-3)/2
G.f.: x / ((1 - x) * (1 - 2*x + x^4)). a(n) = 2*a(n-1) - a(n-4) + 1. - Michael Somos, Dec 28 2012
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EXAMPLE
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a(5)=5+15+7+3=30
x + 3*x^2 + 7*x^3 + 15*x^4 + 30*x^5 + 58*x^6 + 110*x^7 + 206*x^8 + 383*x^9 + ...
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MATHEMATICA
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Join[{c=0}, a=b=0; Table[z=b+a+c+n; a=b; b=c; c=z, {n, 1, 40}]] (*From Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)
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PROG
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(PARI) { a=a1=a2=a3=0; for (n=0, 300, write("b062544.txt", n, " ", a+=n + a2 + a3); a3=a2; a2=a1; a1=a ) } [From Harry J. Smith, Aug 08 2009]
(PARI) {a(n) = if( n<0, n = -n; polcoeff( x^4 / ((1 - x) * (1 - 2*x^3 + x^4)) + x * O(x^n), n), polcoeff( x / ((1 - x) * (1 - 2*x + x^4)) + x * O(x^n), n))} /* Michael Somos, Dec 28 2012 */
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CROSSREFS
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n plus sum of all previous terms gives A000225, n plus sum of two previous terms gives A001924, n plus previous term gives A000217, n gives A001477.
Cf. A007800.
Cf. A119407.
Sequence in context: A209816 A182726 A023610 * A120411 A224520 A069112
Adjacent sequences: A062541 A062542 A062543 * A062545 A062546 A062547
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley, Jun 26 2001
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STATUS
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approved
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