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Search: id:A023531
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| A023531 |
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a(n) = 1 if n of form m(m+3)/2, otherwise 0. |
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+0
60
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| 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; listen)
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OFFSET
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0,1
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COMMENT
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Can read as table: a(n,m)= 1 if n=m >= 0, else 0 (unit matrix).
a(n) = number of 1's between successive 0's (see also A005614, A003589 and A007538) - Eric Angelini (eric.angelini(AT)kntv.be), Jul 06 2005
Triangle T(n,k), 0<=k<=n, read by rows, given by A000004 DELTA A000007 where DELTA is the operator defined in A084938 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2009]
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LINKS
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W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Eric Weisstein's World of Mathematics, Jacobi Theta Functions [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 2009]
Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 2009]
Index entries for characteristic functions
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FORMULA
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If (floor(sqrt(2*n))-(2*n/(floor(sqrt(2*n)))) = -1, 1, 0). - Gerald Hillier, Sep 11 2005
a(n)=1 - A023532(n); a(n)=1 - mod(floor(((10^(n+2) - 10)/9)10^(n+1 - binomial(floor((1+sqrt(9+8n))/2), 2) - (1+floor(log((10^(n+2) - 10)/9, 10))))), 10) - Paul Barry (pbarry(AT)wit.ie), May 25 2004
a(n)=floor((sqrt(9+8n)-1)/2)-floor((sqrt(1+8n)-1)/2). - Paul Barry (pbarry(AT)wit.ie), May 25 2004
a(n)=round(sqrt(2n+3))-round(sqrt(2n+2)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 06 2007
a(n)=ceiling(2*sqrt(2n+3))-floor(2*sqrt(2n+2))-1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 06 2007
a(n)=Sum_{k=1..oo}{C((n+2^(2*k)-k^2/2-k/2-1)^(2*k),n+2^(2*k)-k^2/2-k/2+1) mod 2} - Paolo P. Lava (ppl(AT)spl.at), Sep 07 2007
Contribution from Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Jun 29 2009: (Start)
G.f. 1/2 x^{-1/8}theta_2(0,x^{1/2}), where theta_2 is a Jacobi theta function.
G.f. for triangle: Sum T(n,k) x^n y^k = 1/(1-x*y). Sum T(n,k) x^n y^k / n! = Sum T(n,k) x^n y^k / k! = exp(x*y). Sum T(n,k) x^n y^k / (n! k!) = I_0(2*sqrt(x*y)), where I is the modified Bessel function of the first kind. (End)
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EXAMPLE
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As a triangle:
......1
.....0.1
....0.0.1
...0.0.0.1
..0.0.0.0.1
.0.0.0.0.0.1
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CROSSREFS
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Cf. A000217, A010054.
Sequence in context: A074381 A128407 A134286 this_sequence A089495 A114482 A127829
Adjacent sequences: A023528 A023529 A023530 this_sequence A023532 A023533 A023534
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KEYWORD
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nonn,easy,tabl,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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