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Search: id:A059169
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| A059169 |
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Number of partitions of n into 3 parts which form the sides of a nondegenerate isosceles triangle. |
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+0
14
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| 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 6, 7, 7, 8, 7, 8, 8, 9, 8, 9, 9, 10, 9, 10, 10, 11, 10, 11, 11, 12, 11, 12, 12, 13, 12, 13, 13, 14, 13, 14, 14, 15, 14, 15, 15, 16, 15, 16, 16, 17, 16, 17, 17, 18, 17, 18, 18, 19, 18, 19, 19, 20, 19, 20, 20
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Also number of 0's in n-th row of triangle in A071026. - Hans Havermann (pxp(AT)rogers.com), May 26 2002
Conjecture: this is 0 followed by A026922. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 05 2008]
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FORMULA
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a(n)=C[a(n-1),a(n-2)]-(-1)^n*C[a(n-2),a(n-3)], with a(0)=0, a(1)=0, a(2)=1. - Paolo P. Lava (ppl(AT)spl.at), Feb 25 2008
a(n)=a(n-1)+a(n-4)-a(n-5). G.f.: x^3*(1-x+x^2)/(1-x-x^4+x^5). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 29 2001
Exponent of 2 in factorization of A030436(n-1) and A026655(n-1). First differences of A056837. - R. Stephan, Mar 21 2004
a(n)=-1/8-[1/8+(1/8)*I]*I^n+(3/8)*(-1)^n+(1/4)*n-[1/8-(1/8)*I]*(-I)^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Oct 03 2008]
Euler transform of length 6 sequence [ 0, 1, 1, 1, 0, -1]. - Michael Somos Oct 14 2008
a(3 - n) = -a(n). - Michael Somos Oct 14 2008
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EXAMPLE
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Consider the number 13. The following partitions give a nondegenerate triangle: 4 4 5; 3 5 5; 1 6 6; 2 5 6; 3 4 6. Since the first three partitions represent isosceles triangles, we have A059169(13)=3.
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MAPLE
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a[1] := 0:a[2] := 0:a[3] := 1:a[4] := 0:a[5] := 1:for n from 6 to 300 do a[n] := a[n-1]+a[n-4]-a[n-5]:end do:seq(a[i], i=1..300);
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PROGRAM
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(PARI) {a(n) = (n - 1) \ 2 - (n \ 4)} /* Michael Somos Oct 14 2008 */
(PARI) {a(n) = if( n<1, -a(3 - n), polcoeff( x^3 * (1 - x + x^2) / (1 - x - x^4 + x^5) + x * O(x^n), n))} /* Michael Somos Oct 14 2008 */
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CROSSREFS
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Essentially the same as A008624.
A059169(n) = A005044(n)-A005044(n-9).
A004526(n) = a(2*n + 2) = a(2*n - 1).
Sequence in context: A029363 A033922 A008624 this_sequence A026922 A161090 A027349
Adjacent sequences: A059166 A059167 A059168 this_sequence A059170 A059171 A059172
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KEYWORD
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nonn,easy
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Jan 13 2001
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EXTENSIONS
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More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Mar 25 2002
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