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Search: id:A007584
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| A007584 |
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9-gonal (or enneagonal) pyramidal numbers: n(n+1)(7n-4)/6.
(Formerly M4695)
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+0
5
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| 0, 1, 10, 34, 80, 155, 266, 420, 624, 885, 1210, 1606, 2080, 2639, 3290, 4040, 4896, 5865, 6954, 8170, 9520, 11011, 12650, 14444, 16400, 18525, 20826, 23310, 25984, 28855, 31930
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 194.
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FORMULA
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a(n)= (7*n-4)*binomial(n+1, 2)/3. G.f.: x*(1+6*x)/(1-x)^4.
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MAPLE
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a:=n->sum((n+j)^2-(n+j), j=0..n): seq(a(n)/2, n=0..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 26 2008
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MATHEMATICA
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f[n_]:=7*n+1; s1=s2=0; lst={}; Do[a=f[n]; s1+=a; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 25 2009]
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CROSSREFS
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Cf. A093564 ((7, 1) Pascal, column m=3). Partial sums of A001106.
Sequence in context: A002601 A020495 A008527 this_sequence A009924 A019257 A020877
Adjacent sequences: A007581 A007582 A007583 this_sequence A007585 A007586 A007587
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KEYWORD
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easy,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.
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