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Search: id:A133476
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| A133476 |
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Sum_{ k >= 0} binomial(n,5*k+1). |
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+0
6
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| 0, 1, 2, 3, 4, 5, 7, 14, 36, 93, 220, 474, 948, 1807, 3381, 6385, 12393, 24786, 50559, 103702, 211585, 427351, 854702, 1698458, 3368259, 6690150, 13333932, 26667864, 53457121, 107232053, 214978335, 430470899, 860941798, 1720537327, 3437550076, 6869397265
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 14 2009: (Start)
M^n * [1,0,0,0,0] = [A139398(n), A139761(n), A139748(n), A139714(n), a(n)]
where M = a 5x5 matrix [1,1,0,0,0; 0,1,1,0,0; 0,0,1,1,0; 0,0,0,1,1; 1,0,0,0,1]
Sum of terms = 2^n. Example: M^6 * [1,0,0,0,0] = [7, 15, 20, 15, 7] = 2^6 = 64. (End)
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FORMULA
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a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5).
Sequence is identical to its fifth differences.
O.g.f.: x*(x-1)^3/((2*x-1)*(x^4-2*x^3+4*x^2-3*x+1)) = (1/5)*(3*x^3-7*x^2+6*x-1)/(x^4-2*x^3+4*x^2-3*x+1)-(1/5)/(2*x-1) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2007
Starting (1, 2, 3, 4, 5, 7,...) = binomial transform of (1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 03 2008
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CROSSREFS
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Cf. A049016.
Sequence in context: A048317 A037398 A048331 this_sequence A131023 A069514 A101012
Adjacent sequences: A133473 A133474 A133475 this_sequence A133477 A133478 A133479
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Nov 29 2007
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EXTENSIONS
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Better definition from N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2008
Edited by N. J. A. Sloane (njas(AT)research.att.com), Jul 02 2008 at the suggestion of R. J. Mathar
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