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Search: id:A008498
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| A008498 |
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4-dimensional centered tetrahedral numbers. |
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+0
2
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| 1, 6, 21, 56, 126, 251, 456, 771, 1231, 1876, 2751, 3906, 5396, 7281, 9626, 12501, 15981, 20146, 25081, 30876, 37626, 45431, 54396, 64631, 76251, 89376, 104131, 120646, 139056, 159501, 182126
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of (1,5,10,10,5,0,0,0,....) - Paul Barry (pbarry(AT)wit.ie), Jul 01 2003
If X is an n-set and Y a fixed 5-subset of X then a(n-5) is equal to the number of 5-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Jul 30 2007
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LINKS
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Milan Janjic, Two Enumerative Functions
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FORMULA
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Expansion of (1-x^5 )/(1-x)^6.
a(n)=C(n, 0)+5C(n, 1)+10C(n, 2)+10C(n, 3)+5C(n, 4); a(n)=(5n^4+10n^3+55n^2+50n+24)/24. - Paul Barry (pbarry(AT)wit.ie), Jul 01 2003
a(n)=binomial(n+5,5)-binomial(n,5). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 21 2006
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MAPLE
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[seq(binomial(n+5, 5)-binomial(n, 5), n=0..45)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 21 2006
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CROSSREFS
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Sequence in context: A132366 A015641 A050190 this_sequence A015640 A138780 A108907
Adjacent sequences: A008495 A008496 A008497 this_sequence A008499 A008500 A008501
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KEYWORD
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nonn
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AUTHOR
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njas
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