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Search: id:A139398
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| A139398 |
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Sum_{ k >= 0} binomial(n,5*k). |
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+0
5
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| 1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 254, 474, 859, 1574, 3004, 6008, 12393, 25773, 53143, 107883, 215766, 427351, 843756, 1669801, 3321891, 6643782, 13333932, 26789257, 53774932, 107746282, 215492564, 430470899, 859595529, 1717012749, 3431847189, 6863694378
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 13 2009: (Start)
M^n * [1,0,0,0,0] = [a(n), A139761(n), A139748(n), A139714(n), A133476(n)]
where M = the 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]; sum = 2^6 = 64. (End)
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FORMULA
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G.f.:-(x-1)^4/((2*x-1)*(x^4-2*x^3+4*x^2-3*x+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
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MAPLE
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f:=(n, r, a) -> add(binomial(n, r*k+a), k=0..n); fs:=(r, a)->[seq(f(n, r, a), n=0..40)];
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CROSSREFS
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Cf. A024493-A024495, A038503-A038505, A000749, A133476, A139714, A139748, A139761.
Sequence in context: A153527 A153556 A099132 this_sequence A099131 A063019 A018039
Adjacent sequences: A139395 A139396 A139397 this_sequence A139399 A139400 A139401
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2008
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