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Search: id:A060432
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| 1, 3, 5, 8, 11, 14, 18, 22, 26, 30, 35, 40, 45, 50, 55, 61, 67, 73, 79, 85, 91, 98, 105, 112, 119, 126, 133, 140, 148, 156, 164, 172, 180, 188, 196, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 295, 305, 315, 325, 335, 345, 355, 365, 375, 385, 396, 407, 418
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In other words, first differences give A002024.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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Let f(n) = floor(1/2 + sqrt(2*n)), then this function is S(n) = f(1) + f(2) + f(3) + ... + f(n).
a(n) is asymptotic to c*n^(3/2) with c=0.9428.... - Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 18 2002
a(n) is asymptotic to c*n^{3/2} with c = (2/3)*sqrt(2) = .942809.... - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Sep 07 2006
Set R=ROUND(SQRT(2*n),0), then a(n)=((6*n+1)*R-R^3)/6 [From Gerald Hillier (adr.rabbicat(AT)gmail.com), Nov 28 2008]
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EXAMPLE
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a(7) = 1 + 2 + 2 + 3 + 3 + 3 + 4 = 18
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PROGRAM
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(PARI) f(n) = floor(1/2+sqrt(2*n)) for(n=1, 100, print1(sum(k=1, n, f(k)), ", "))
(PARI) { default(realprecision, 100); for (n=1, 1000, a=sum(k=1, n, floor(1/2 + sqrt(2*k))); write("b060432.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 05 2009]
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CROSSREFS
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Cf. A002024.
Sequence in context: A052488 A076372 A005356 this_sequence A156023 A062009 A062484
Adjacent sequences: A060429 A060430 A060431 this_sequence A060433 A060434 A060435
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KEYWORD
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easy,nonn
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AUTHOR
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Robert A. Stump (bobess(AT)netzero.net), Apr 06 2001
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EXTENSIONS
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More terms from Jason Earls (zevi_35711(AT)yahoo.com), Jan 08 2002
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