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Search: id:A058187
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| A058187 |
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Expansion of (1+x)/(1-x^2)^4: duplicated tetrahedral numbers. |
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+0
5
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| 1, 1, 4, 4, 10, 10, 20, 20, 35, 35, 56, 56, 84, 84, 120, 120, 165, 165, 220, 220, 286, 286, 364, 364, 455, 455, 560, 560, 680, 680, 816, 816, 969, 969, 1140, 1140, 1330, 1330, 1540, 1540, 1771, 1771, 2024, 2024, 2300, 2300, 2600, 2600, 2925, 2925, 3276, 3276
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = A108299(n-3,n)*(-1)^floor(n/2) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 01 2005
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FORMULA
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a(n) =A006918(n+1)-a(n-1). a(2n)=a(2n+1)=A000292(n)=(n+1)*(n+2)*(n+3)/6.
a(n)=(2n^3+21n^2+67n+63)/96+(n^2+7n+11)(-1)^n/32. - Paul Barry (pbarry(AT)wit.ie), Aug 19 2003
Euler transform of finite sequence [1, 3]. - Michael Somos Jun 07 2005
G.f.: 1/((1-x)*(1-x^2)^3). a(n)=-a(-7-n).
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PROGRAM
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(PARI) a(n)=binomial(n\2+3, 3) /* Michael Somos Jun 07 2005 */
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CROSSREFS
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Cf. A057884. Sum of 2 consecutive terms gives A006918, whose sum of 2 consecutive terms gives A002623, whose sum of 2 consecutive terms gives A000292, which is this sequence without the duplication. Continuing to sum 2 consecutive terms gives A000330, A005900, A001845, A008412 successively.
Cf. A096338.
Sequence in context: A140234 A101256 A116569 this_sequence A006477 A058596 A050339
Adjacent sequences: A058184 A058185 A058186 this_sequence A058188 A058189 A058190
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Nov 20 2000
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