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0, 0, 0, 1, 3, 5, 7, 10, 14, 18, 22, 27, 33, 39, 45, 52, 60, 68, 76, 85, 95, 105, 115, 126, 138, 150, 162, 175, 189, 203, 217, 232, 248, 264, 280, 297, 315, 333, 351, 370, 390, 410, 430, 451, 473, 495, 517, 540, 564, 588, 612, 637, 663, 689, 715, 742, 770, 798
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Column sums of an array of the odd numbers repeatedly shifted 4 places to the right:
1 3 5 7 9 11 13 15 17...
1 3 5 7 9...
1...
.........................
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1 3 5 7 10 14 18 22 27...
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (3,-4,4,-3,1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2010]
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FORMULA
| G.f.: x^3(1-x^2)/((1-x)^3(1-x^4)).
G.f.: x^3/((1+x^2)*(1-x)^3) - Jon Perry (perry(AT)globalnet.co.uk), Mar 31 2004
a(n) = +3*a(n-1) -4*a(n-2) +4*a(n-3) -3*a(n-4) +a(n-5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 15 2010]
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MAPLE
| seq(floor(binomial(n, 2)/2), n=0..57); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 12 2009]
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MATHEMATICA
| a = 0; Join[{b = 0, c = 0}, Table[d = n^2 - a - b - c; a = b; b = c; c = d, {n, 0, 120}]] (* From Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)
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PROG
| (PARI) a(n)=binomial(n, 2)\2
(Other) sage: [floor(binomial(n, 2)/2) for n in xrange(0, 58)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 01 2009]
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CROSSREFS
| A054925(n)=a(-n). A035608(n)=a(2n+1).
A column of triangle A011857.
First differences are in A004524.
Sequence in context: A194170 A194166 A054040 * A131673 A151945 A140261
Adjacent sequences: A011845 A011846 A011847 * A011849 A011850 A011851
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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